It is common knowledge/understanding that Lord Krishna showed the Vishwaroopa to Arjuna at his request.
A video (1:23-1:59) says that it is Lord Shiva who showed the Vishwaroop.
What is the actual fact? Who showed the Vishvaroop?
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Let's see, to understand it I have to divide my answer into 2 parts. The 1st part being the summary and links to my previous answers and some texts and the 2nd part addressing the question to some extent and concluding it. The links are given to grasp the full context and for shortening this answer, otherwise it will turn into a blog. Hope the readers will read the post. Still i will give 1-liner summary.
Bhagwad Gita is the retelling of Ishwara Gita and Lord Krishna himself told to Arjuna he can't repeat it when asked, as he was connected with Brahman in yoga while giving the knowledge. So, instead he gave him Anu Gita which mainly focuses on Yoga.
Lord Vishnu always remains in a yogic connection with Bhagawan Shiva and his own Chaturbhuja form is an illusion and his real form is that of 5-faced Lord Maheshwara and 18 chapters of Gita are the body parts of Bhagawan Panchavakra Maheshwara.
“esha vidhwan guna sreshto Vishnu parama durjaya | divya chakshur maha theja veekshyathe yoga chakshsha |” (MBH 13:14:9).
“Bhishma said.: That Vishnu (Krishna) who knows every thing, who has greatest qualities, who cannot be won over by anybody, who has special holy sight, and who is greatly resplendent, always sees and remains connected (viz meditate on) him (Rudra) by his eyes of yoga”.
Lord Vishnu showed his Virat roop to Sage Dadhichi, who in return showed him his own Virat Roop in Sri Shiva Purana 2.2:2:39.:
In point no. 2 it's clear that Lord Vishnu's form is illusional, and in Mahabharata everyone knew Lord Krishna as an avatar of Lord Vishnu even Duryadhana, who called him by the names such as slayer of Madhu, etc etc that's why in B.G. Arjuna in many Places called that form as Vishnu as he also knew the same. So, he also, asked for forgiveness to treat Lord Krishna as a friend even though he himself was the Nara Avatara of Lord Vishnu.
In above point no. 5 when sage Utanka saw the Vaishnava Form of Lord Krishna he prayed to him with wonder and devotion instead of fear like Arjuna who got terrified seeing the form and the prayer is totally focussed only on the two factors viz. – Firstly, the all pervasive nature of the form and second, Vishnu’s glorification by various names of his, such as ‘padmanabha’ etc. This is purely Vishnu’s form, and there is no depiction of terrible fangs and mouths devouring entire creation grinding them under the sharp teeth etc.
This point gives yet another strong evidence in support of my view as follows – Uttanka on seeing the divine ‘vaishnava’ form, clearly recognized it as ‘vishnu’ and sang praises in his glorification which were ‘vishnu specific’ using various names such as – narayana, padmanabha, madhava, vasudeva etc. Whereas contrasting with Bhagawad Gita’s cosmic form we see that, Arjuna could not clearly recognize whom he was witnessing. Arjuna asked that lord to reveal who he was, as quoted in below verse.
“ākhyāhi me ko bhavānugrarūpo namo’stu te devavara prasīda। vijñātumicchāmi bhavantamādyaṃ na hi prajānāmi tava pravṛttim॥“ (MBH 6:35:31).
“Tell me who thou art of (such) fierce form. I bow to thee, O chief of the gods, be gracious to me. I desire to know thee that art the Primeval One, I do not understand thy action”.
And in reply to his question, in the immediately next verse, the lord says – “I am ‘kala’”.
“śrībhagavānuvāca kālo’smi lokakṣayakṛtpravṛddho lokānsamāhartumiha pravṛttaḥ॥” (MBH 6:35:32a).
“The Holy One said, “I am ‘kāla (Time)’, the destroyer of the worlds, fully developed. I am now engaged in slaying the race of men”.
“His (Shiva’s) works are said to be uncanny because he (alone) carries out creation, preservation and destruction. He is the one who cut brahma’s head. He is the father of Brahma as well as his son. Similarly, He is the father of Vishnu as well as his son and he is also the controller of Vishnu. He confers knowledge on these two – Brahma and Vishnu and always showers his grace (upon them)”.( Sri Shiva Purana 7:02:31:121-122).
Which is also in sync with vedas.
“He (Kāla) surely did bring hither all the beings (worlds), he surely did encompass all the beings (worlds). Being their father, he became their son; there is, verily, no other force, higher than he” (Atharva Veda 19:53:4).
“Kesava (Krishna) is that devoted worshipper of Rudra who has sprung from Rudra himself. Kesava always worships the Lord Siva, regarding his Linga emblem to be the origin of the universe. The God having the bull for his mark cherisheth greater regard for Kesava”. (MBH 7:172:89-90).
"O the lord of lord! Myself (Krishna/Vishnu), brahma, kapila, ananta (sheSha), all the valiant sons of brahma who conquered over the internal enemies - all are created from you (Shiva). Hence you are the lord of all. Hence you, the lord of all, are only worthy of praise and worship." (Harivamsa Parva 2-74-34).
“yatra sarvakṣayaṃ kṛtvā tāvubhau rāmakeśavau। nāticakrāmatuḥ kālaṃ prāptaṃ sarvaharaṃ mahat॥” (MBH 1:2:350).
“In this, both Balarama and Kesava (Krishna) after causing the extermination of their race, their hour having come, themselves did not rise superior to the sway of all-destroying Kala”.
So, yes, it is correct that Bhagawad Gita’s form was that of Bhagwan MahaKala and Mahakala’s fear inspiring ‘ghora’ form superimposed over Vishnu’s all-pervasive ‘soumya’ form. Hence Arjuna had definitely seen the vaishnava form but that was possessed by Mahakala’s form hence was extremely terrible to behold at.
The supreme lord in Bhagawad Gita tells Arjuna who he is. He clearly says that he is the supreme ‘Kala’. This Kala is not ‘Yama’, rather, is the supreme ‘Mahakala’ the very destructive aspect of Bhagawan Shiva. The lord says that he has already slain all the enemies of Arjuna such as ‘Bhishma, Drona, Karna etc.’ and tells Arjuna that Arjuna was just an instrument who was visible in this world engaging in killing.
“śrībhagavānuvāca kālo’smi lokakṣayakṛtpravṛddho lokānsamāhartumiha pravṛttaḥ। ṛte’pi tvāṃ na bhaviṣyanti sarve ye’vasthitāḥ pratyanīkeṣu yodhāḥ॥ 32 tasmāttvamuttiṣṭha yaśo labhasva jitvāśatrūnbhuṅkṣva rājyaṃ samṛddham। mayaivaite nihatāḥ pūrvameva nimittamātraṃ bhava savyasācin॥ 33 droṇaṃ ca bhīṣmaṃ ca jayadrathaṃ ca karṇaṃ tathānyānapi yodhavīrān। mayā hatāṃstvaṃ jahi mā vyathiṣṭhā yudhyasva jetāsi raṇe sapatnān॥” (MBH 6:35:32-34).
“The Holy One said, “I am ‘kāla (Time or Death)’, the destroyer of the worlds, fully developed. I am now engaged in slaying the race of men. Without thee all these warriors standing in the different divisions shall cease to be. Wherefore, arise, gain glory, (and) vanquishing the foe, enjoy (this) swelling kingdom. By me have all these been already slain. Be only (my) instrument. O thou that can’st draw the bow with (even) the left hand. Drona and Bhishma, and Jayadratha, and Karna, and also other heroic warriors, (already) slain by me, do thou slay. Be not dismayed, fight; thou shalt conquer in battle (thy) foes”.
The same is narrated by Krishna in Shanti Parva in chapter 342. Krishna tells to Arjuna the same fact which Vyasa had also revealed to Arjuna earlier. He says that Rudra is known as “Kala” and tells Arjuna that all the foes that Arjuna had slain, had actually been slain beforehand by Kala (Rudra). Therefore relating both these instances we can easily understand that the terribel cosmic form displayed in Bhagavad Gita instance was Mahakala form of bhagavan Rudra!
“yastu tē sō’gratō yāti yuddhē sampratyupasthitē. taṁ viddhi rudraṁ kauntēya dēvadēvaṁ kapardinam. 138 kālaḥ sa ēva kathitaḥ krōdhajēti mayā tava.. nihatāstēna vai pūrvaṁ hatavānasi yānripūn.139 apramēyaprabhāvaṁ taṁ dēvadēvamumāpatim. namasva dēvaṁ prayatō viśvēśaṁ haramakṣayam |” (MBH 12:342:138-140).
“That Being whom, at the time of all thy battles, thou beheldest stalking in thy van, know, O son of Kunti, is no other than Rudra, that god of gods, otherwise called by the name of Kaparddin. He is otherwise known by the name of Kala, and should be known as one that has sprung from my wrath. Those foes whom thou hast slain were all, in the first instance, slain by him. Do thou bend thy head unto that god of gods, that lord of Uma, endued with immeasurable puissance. With concentrated soul, do thou bend thy head unto that illustrious Lord of the universe, that indestructible deity, otherwise called by the name of Hara."
In Ishvara Gita also, lord Shiva exhibits his supreme nataraja cosmic form having thousands of head, thousands of feet and dances in the firmament. In Shiva’s ‘vama-bhaga’ (left side) remains Vishnu (because he is in fact Shiva’s wife Uma in male form) This Forminf a ShivaLingam. Bhagawan Shiva is described in Ishvara Gita as having terrible fangs and sharp teeth as follows.
“brahmāṇḍaṃ tejasā svena sarvamāvṛtya ca sthitam | daṃṣṭrākarālaṃ durdharṣaṃ sūryakoṭisamaprabham ||” (Kurma purana_2,5.10).
“The one who is established in the world with his own lustre, who has the terrible fangs, which are aweful possessing the lustre of crores of suns”.
This is in similar fashion (although may not necessarily be same, as these forms are all formed of Maya and are taken for specific purposes) seen in Bhagawad Gita also.
“daṃṣṭrākarālāni ca te mukhāni dṛṣṭvaiva kālānalasannibhāni। diśo na jāne na labhe ca śarma prasīda deveśa jagannivāsa॥“ (MBH 6:35:25).
“Beholding thy mouths that are terrible in consequence of (their) fangs, and that are fierce (as the all-destroying fire at the end of the Yuga), I cannot recognise the points of the horizon nor can I command peace of mind. Be gracious, O God of gods, O thou that art the refuge of the Universe”.
Even if we see the events in the destruction of Daksha’s sacrifice, Veerabhadra is always shown as having terrible fangs and sharpened teeth. That is a trademark awful form of Mahakala aspect of lord Shiva. So, lord Shiva had shown his Mahakala form over his Nataraja aspect to sages in Ishvara Gita; whereas in the battlefield of Kurukshetra he had shown his terrible Mahakala form on top of the all-pervasive form to Arjuna.
Now, the verse in question.
It's totally authentic and is Present in Sri Kurma Purana itself where the Original Srimad Ishwara Gita is Present.
In Kurma Purana, there is yet another chapter where Vyāsa and Arjuna converse on the topic of symptoms and duties of Kali age. In that chapter, Vyāsa stresses many a times on the necessity of worship of Lord Rudra, and finally with much delight Vyāsa touches Arjuna with both his hands and calling him as the greatest of the devotees of Shiva praises him for being the luckiest to have witnessed the cosmic form of lord Shiva during the Bhagavad Gītā discourse that hṛṣīkeśa spoke to him.
“dṛṣṭavānasi taṃ devaṃ viśvākṣaṃ viśvatomukham | pratyakṣameva sarveśaṃ rudraṃ sarvajaganmayam ||60 jñānaṃ tadaiśvaraṃ divyaṃ yathāvad viditaṃ tvayā | svayameva hṛṣīkeśaḥ prītyovāca sanātanaḥ ||” (Kurma Purana 1:28:61).
“[Vyasa says].:You have directly perceived that (Universal form of) Lord Rudra who has his eyes everywhere, who has his faces everywhere, who is the very embodiment of the universe. That divine lordly knowledge (of śiva) has been precisely understood by you. That ancient Hrsikesha (Krishna) himself had recounted it to you out of delight”.
The ‘ishvara gita’, which was originally discoursed by Bhagawan Shiva, and which was transmitted by various other personalities to sages mentioned there, in same lines, it is been said that, Lord Narayana also himself as Krishna, the son of Devaki had discoursed this Ishwara Gita to Arjuna.
“nārāyaṇo ‘pi bhagavān devakītanayo hariḥ | arjunāya svayaṃ sākṣāt dattavānidamuttamam ||” (kurma purana 2:11:131).
“Also the lord Narayana, who is called Hari, had himself passed on that excellent knowledge (of Srimad Ishwara Gita of Bhagawan Shiva) to Arjuna in the form of Krishna, the son of devaki”.
Conclusion.: B.G. Vishwaroop was a Mixture of Vaishnava Saumya form as Yoni and MahaKala Ugra-Ghora form as Linga.
I hope this clarifies all your queries. Prd..
Answer is it is Krishna's vishwaroopa unless Lord Shiva is same as Lord Krishna. Also in Vedas and other texts it is common to use the name of another deity to refer to the intended deity. But clearly this is not the opinion of the speaker in the video since his argument is Lord Krishna versus Lord Shiva. Hence that possibility can be ruled out.
With this assumption below are the reasons to my conclusion.
पश्यामि देवांस्तव देव देहे सर्वांस्तथा भूतविशेषसङ्घान्। ब्रह्माणमीशं कमलासनस्थ - मृषींश्च सर्वानुरगांश्च दिव्यान्॥ ११ - १५॥
The speaker in the video quotes "Poorva Purana" as his source. I assume he is referring to Adi Purana by Jinasena (9th Century AD) since it is mentioned in Wikipedia that Shaiva philosophy was inspired by this work. Hence as @Vivikta commented the source itself is sectarian and not authoritative like Lord Vedavyasa's original 18 puranas. Hence one can expect bias towards Lord Shiva.
If you observe the part of the video the author of this question has mentioned, the speaker argues that Lord Shiva cannot be part of the Vishwaroopa since he himself is the exhibitor of it. In the later part of the lecture he solidifies the argument by saying "ब्रह्माणमीशं" in the same shloka refers to only Lord Brahma sitting on the lotus who himself is given the adjective of "Isha" or Lord. In other words Isha is not referring to Shiva in this context but Brahma himself.
पश्यामि देवांस्तव देव देहे सर्वांस्तथा भूतविशेषसङ्घान्। ब्रह्माणमीशं कमलासनस्थ - मृषींश्च सर्वानुरगांश्च दिव्यान्॥ ११ - १५॥
Basically the logic presented here is that the exhibitor himself cannot be part of the exhibit. First of all this is not always true - recall that Krishna showed the entire universe including Himself and His mother who is watching it inside his mouth. Anway going by his logic the divine form of Lord Krisha should be visible inside this Vishwaroopa just like Brahma and others. But it is nowhere mentioned so. In fact Arjuna prays "Vishwamoorthi" to "reduce" to his divine form with the Lord Vishnu's characteristic Chakra and four arms.
किरीटिनं गदिनं चक्रहस्तं इच्छामि त्वां द्रष्टुमहं तथैव । तेनैव रूपेण चतुर्भुजेन सहस्रबाहो भव विश्वमूर्ते ॥ ११ - ४६॥
दृष्ट्वेदं मानुषं रूपं तव सौम्यं जनार्दन । इदानीमस्मि संवृत्तः सचेताः प्रकृतिं गतः ॥ ११ - ५१॥
When Arjuna asked Sri Krishna to show his Divine form (द्रष्टुमिच्छामि ते रूपमैश्वरं पुरुषोत्तम), Sri Krishna says as follows:
पश्य मे पार्थ रूपाणि शतशोऽथ सहस्रशः।
नानाविधानि दिव्यानि नानावर्णाकृतीनि च।।11.5।।
O Arjuna, forms of Mine, by the hundreds and thousands, of different sorts, divine, and of various colours and shapes.
इहैकस्थं जगत्कृत्स्नं पश्याद्य सचराचरम्।
मम देहे गुडाकेश यच्चान्यद्द्रष्टुमिच्छसि।।11.7।।
Now behold, O Arjuna, in this, My body, the whole universe centred in one including the moving and the unmoving and whatever else thou desirest to see.
Krishna showed Arjuna his vishwarupa.
Specifically, relating to the Gita verse 11.15 mentioned in the video link given in the question, two famous modern Indian translations/meanings are presented below.
1. Meaning (tAtparya)taken from Samskrita Bharati's Gita Pravesha book
Book description image
This interprets the word Isham as referring to Parvati Pati Shiva.
2. Gita press translation
Book description image
Both translations agree that Parvati Pati Shiva is present in the Vishwaroopa. It is unthinkable that Samskrita Bharati pandits don't know Sanskrit or that Gita Press and Samskrita Bharati would cause insult to any Hindu God. The safer alternative is to assume that the translations/interpretations are valid. (This does not mean other translations are invalid).
This also shows that the Vishwaroopa displayed in the Gita belongs to Krishna.