"Prana," this word being the Sanskrit term meaning "Absolute Energy."
Science of Breath, by Yogi Ramacharaka, William Atkinson, 
What is Prana? Prana is the center of everything.
"Prana is Fire; Prana is the Sun; the Cloud; the Wind; Prana is the Killer of Demons; Prana is the Earth. It is what is and is not, immortal. Prana is the center of everything."
Brahma, in the earlier Vedic books, is a neuter noun, meaning the spell or prayer of the priest and the magic power which it exerts over gods, men, and the universe. Prāṇa, again, is properly the breath of the body, hence the incorporeal forces or functional energies on which depends the existence of material life.
Brahma Knowledge, 1911
Homage to Prāna, him who hath dominion o'er the universe,
Who hath become the Sovran Lord of all, on whom the whole depends!
Homage, O Prāna, to thy roar, to thunder-peal and lightning flash!
Homage, O Prāna, unto thee what time thou sendest down thy rain!
When Prāna with a thunderous voice shouts his loud message to the
plants, They straightway are impregnate, they conceive, and bear
When the due season hath arrived and Prāna shouteth
Then all is joyful, yea, each thing upon the surface of
When Prāna hath poured down his flood of rain upon the
Hymns of the Atharva Veda, translated by Ralph T.H. Griffith, , Book 11, Hymn 4
Rishi Markandeya said to Yudhisthir, "The Prana and the Apana air are interposed within the Samana and the Udana air. And the heat generated by their coalition causes the growth of the body (consisting of the seven substances, bones, muscles, etc.)"
Rishi Markandeya said to Yudhisthir, "While seated here (in a corporeal frame) it is sustained in all its relations external or internal (to matter or mind) by the subtle ethereal air called prana".
Mahabharat, Vana Parva (Book 3), Markandeya-Samasya Parva (Section CCXIII), by Mohan Ganguli, tr. [1883-1896]
He(Prana) moves as an embryo within the gods; having arrived, and being in existence, he is born again. Having arisen he enters with his mights the present and the future, as a father (goes to) his son.
They call Prâna Mâtarisvan (the wind); Prâna, forsooth, is called Vâta (the wind). The past and the future, the all, verily is supported upon Prâna.
The holy (âtharvana) plants, the magic (ângirasa) plants, the divine plants, and those produced by men, spring forth, when thou, O Prâna, quickenest them.
May Prâna, who rules over this (all) derived from every source, and over everything that moves, (may he) unwearied, strong through the brahma, adhere to me!
First, thou were born of Akasa, then of fire, and then of water.
Brahma who creates by His will and along with its law, comes to an end; all the Akasa (matter) and the Macrocosm merge into the Paramesuara [i.e., Parameshwara—JBH.] (non-dual; the highest God), that which is the liberator from the delusion of illusions .
Yoga Vashishtha, tr. by Rishi Singh Gherwal, 
Gargi said, “Yajnavalkya, that which they say is above heaven and below the earth, which is between heaven and earth as well, and which was, is, and shall be – tell me, in what is it woven, warp and woof?’
Yajnavalkya said, “That of which they say, O Gargi, that it is above heaven and below the earth, which is between heaven and earth as well, and which was, is, and shall be–that is woven, warp and woof, is the ether. “Ether (Akasha) is the subtlest element. So subtle that it is often indistinguishable from Consciousness. Without it nothing can exist. Yet, there is more”.
Brihadaranyaka Upanishad 3:8
From Mahabharat, we know, the prana and the air causes the growth.
Sanskrit term meaning is "Absolute Energy" for Prana.
We know from the Upanishads, and multiple sources of Hindu Scriptures including Atharvaveda, that Prana is all pervading.
From Brihadaranyaka Upanishad, we know Akasha is different from Consciousness and is often indistinguishable. And that "more" is Brahman and Parabrahman.
Also, Yajnavalkya Rishi clears that everything everywhere is woven in Akasha/ether.
Yoga Vasistha says concentrating on Akasha you go beyond matter which in turn would make things like levitation possible for a yogi.
Different from this, which consists of the essence of food, is the other, the inner Self, which consists of breath. The former is filled by this. It also has the shape of man. Like the human shape of the former is the human shape of the latter. Prâna (up-breathing) is its head. Vyâna (back-breathing) is its right arm. Apâna (down-breathing) is its left arm. Ether is its trunk. The earth the seat (the support).
Yajurveda, Section: Taittiriya Upanishad, Second Anuvacha.
From this, which is in accordance to the references presented by you of Swami Vivekanand, he concluded that Akash is acted upon by Prana.
One should take into consideration that there are different levels of enlightenment/ liberation. Similarly, although some people might think he became the all knower/ as he knew His self but that has fundamental flaws in it as he was not the all-knowing.
It is said, if one knows the Brahman, one becomes like the Brahman. And that the one who knows the Atman is freed from everything worldly. There's various levels of knowledge, it's understanding, putting it in practice, and having something called as "Sakshatkar" as well.
One can say everything is created from Brahman. //This is true
One can also say everything is created from Aakash, which is also true! As mentioned in Yajurveda's Taittiriya Upanishad.
One can say everything is from energy, which is true as well.
One can say we are from water. //True
One can say we are from dust(which is Earth)// Christianity, in a way true.
Hinduism says this body is made of five base elements Ether/Aakash/Space, Air, Fire, Water, Earth.// Much more precise.
If you refer Hindu Scriptures you will know, that body has 5 base elements, 5 mahabhut, 5 gnanendriyas, 5 karmendriyas, 4 antaharan - mann, buddhi, chitt, ahankar.
Those belonging to the Sankhya philosophy propound the existence of 24 elements and believe Parmatma to transcend them; i.e. Parmatma is 25th element.
Yoga philosophy propounds that jiva and ishwar is 25th element and Parmatma the 26th.
The point being Swami Vivekanand is not wrong but what he says is according to his understanding of the Vedas and Hindu Scriptures. He never claimed that whatever He is saying is the Ultimate truth and is the only truth or that whatever He says is the only way for Liberation. And of course he has never said that Upanishads or Vedas are false, so if you yourself research Upanishads, and Vedas, you might be able to draw different statements too. And that's why, Bhagwan Swaminarayan and others have said that they need to be understood from a Satpurush as one would be utterly confused if one goes on to understand by himself - just as we see ISIS, etc. to derive their source to kill Non-Muslims from the same book which most people of that community find peace in and do not harbour violence in their hearts probably.
Currently, that Satpurush from whom, every good Scripture can be learnt is Mahant Swami Maharaj.
Only one who realises God through these four scriptures can be said to possess total gnān. For example, only when one sees with one’s eyes does one come to know that milk is white; only when one smells with one’s nose does one come to know its smell; only when one touches it with one’s finger does one come to know whether it is hot or cold; and only when one tastes it with one’s tongue does one come to know its taste. In this manner, only when milk is tested through all of the indriyas can one totally know its nature; it cannot be totally known through one indriya alone. Similarly, one realises God’s nature totally when one realises it through the four scriptures, i.e., the Vedas, etc. To have such knowledge is called total gnān.
Bhagwan Swaminarayan, Vachanamrut, Vartal 2 Full text here
So, I am of the opinion that get what is useful, utilize it, always try to know the bigger picture. This is just one person(Swami Vivekanand) stating one point but the whole philosophies have contradictions with other Hindu philosophies too(Kapil Muni's Sankhya Philosophy and Yoga Philosophy),
The great Acharyas accepted by Hinduism, Ramanujacharya, Shankarachaya, Madhavacharya, Vallabhacharya propounded their own statements and paths to liberation all contradicting to each other yet within Hinduism and all having hundreds of thousands of followers. And the Latest Acharya, who is living right now, the person who wrote a Bhashya and is accepted and respected across Hinduism and propogated a Vaidik-Sanatan Siddhant is Vedant Martand, Darshan Kesari, Mahamahopadhyay Sadhu Bhadreshdas with Akshar Purushottam Darshan which I am a follower of.
Also, because of the references, Swami Vivekanand might have concluded because without energy nothing is possible and without Akash too. Aakash doesn't have a life in itself. Prana does. So, unless Prana acts on Akash technically nothing can be created. The bigger picture being the Brahman making this all happen. And Parabrahman the ultimate reason behind everthing.
You do need to hear what great people have to say!
40 Universities Honor Mahamahopadhyay Swami Bhadreshdasji, Bengaluru, India, 15 Feb 2018
Felicitation by numerous Universities at M S University, Gujarat
Full video to the Bengaluru Felicitation Event of Bhadresh Swami