Here I am trying to figure out answer of your question from Vishnu-Sastranam Strotram, Bhagvad Gita & Sri Ramanujacharaya (Vishitaadvaita) Phiosophy.
So, Let's first we look-out the Sloka
Translation of particualr Sloka of Visnu-Sajasrnam Strotram:
jīvō vinayitāsākṣī mukundōmitavikramaḥ |
meaning:
Jivo:One who as the Kshetragya or knower of the field or the
body, is associated with the Pranas
Vinayitā-sākṣī: One who witnesses the Vinayita or worshipful
attitude of all devotees.
Mukundaḥ: One who bestows Mukti or Liberation.
Amitavikramaḥ: One whose three strides were limitless
Now, we under-stand it from Gita Chapter 13 Sloka 1,2,3:
śrī arjuna uvāca
prakṛtiṃ puruṣaṃ caiva kṣetraṃ kṣetrajñam eva ca |
etad veditum icchāmi jñānaṃ jñeyaṃ ca keśava || 1 ||
Arjuna Asked
O Kesava, I desire to learn about the spirit and about matter, about the Field and its Knower, about
knowledge and the knower.
Śrī Bhagavān uvāca
idaṃ śarīraṃ kaunteya kṣetram ityabhidhīyate |
etad yo vetti taṃ prāhuḥ kṣetrajñā iti tad vidaḥ || 2 ||
The Lord said:
This body, O Arjuna, is called the Field (Kṣetra). One who knows it is called the ‘Knower of
the Field’ (Kṣetrajña), by the enlightened ones.
kṣetrajñaṃ cāpi māṃ viddhi sarva kṣetreṣu bhārata |
kṣetra kṣetrajñayor-jñānaṃ yat tajjñānam mataṃ param || 3 ||
- And know Me also as the Kṣetrajña in all Fields, O Arjuna. The knowledge of both the Field
and its Knower is, in My view, the highest knowledge.
Now, Understand throgh the philosophy of Sri Ramanujacharaya
In reference to the body one says; ‘I am a god’, ‘I am a human’, ‘I am fat’, ‘I am thin’
etc. according to the principle of co-ordinate predication (samānādhikaraṇya) the ‘I’
referred to is the experiencing Self (jivātman), and that which is experienced [as fat, thin
etc] refers to something other than the Self i.e. the body. The enlightened ones
understand that the body is only the Field where the fruits of past deeds are reaped by
the Self, which is different from the body.
It is obvious that when one sees an object like a pot which is different from one's body,
one thinks — 'I, a god, see this pot' or 'I, a human see it' etc., in this case one is
identifying with one’s body by the principle of samānādhikaraṇya. In the same way one
also experiences the body as an object of knowledge when one says:— ‘I know this
body.’ Thus, if the body is a knowable object, it must be different from the knowing
subject. Therefore, the Self as Field-knower (Kṣetrajña), is different from the body
which is an object of knowledge like a pot and other things.
But in practical terms one's body is inseparable from oneself; for it constitutes a
fundamental attribute of the Self like the 'cow-ness' of the cow. The knowing Self is
however unique in being an eternal and subtle form of consciousness and can only
perceive itself through a mind refined by Yoga and not by mundane awareness. The
ignorant regard the Self as being a physical phenomena because of its intimate
involvement with material nature. Sri Krishna thus declares later on:— ‘When, being
associated with the Guṇas, the Self departs or stays or experiences the deluded perceive
it not, only those who are enlightened see’. (15.10).
As the Overself, Krishna is the ‘Field-Knower’ in all the bodies such as those of gods,
humans, animals and antigods. By the expression 'also' (api) it can be inferred that the
body itself is also a manifestation of Krishna. Just as the body cannot exist separately
from the ātman on account of its being an attribute [eg. like the mango and its taste]
and consequently when referring to the body one actually refers to the ātman according
to the principle of co-ordinate predication, in the same manner, both the body (Field)
and the Self (Field-Knower), on account of both of their being inseparable attributes of
Krishna’s can thus be denoted as ‘one with Krishna’.
The Veda teaches that the Supreme Being is the Overself both the Kṣetra (Field) and the
Kṣetrajña (Jīva), because of their being like His ‘body’ [corporeality]. For example see
the passages from the Brhad-aranyaka Upanishad beginning with 3.7.3).
From this Sloka which I mentioned 13.3 kṣetrajñaṃ cāpi māṃ viddhi sarva kṣetreṣu bhārata |
kṣetra kṣetrajñayor-jñānaṃ yat tajjñānam mataṃ param || 3 ||
3. And know Me also as the Kṣetrajña in all Fields, O Arjuna. The knowledge of both the Field
and its Knower is, in My view, the highest knowledge.
The Advaitin claims that this passage teaches absolute identity between the Jīva and Iśvara.
Let's understand it as per the Sri Ramanujacharaya
Rāmānuja’s position is that the relationship is not one of absolute ontological identity but only
one of identity of reference of several inseparable entities to a common substratum — known
technically as Samānādhikaraṇya or co-ordinate predication. The literal meaning of the expression
is 'the relation of abiding in a common substratum'. The relation of the Jīva and Prakrti to Iśvara is
as of body and self or as a mode (Prakara) and its substratum. The relation between the body and
Self of an ordinary being is, only separable at death. But it is inseparable in the case of Iśvara and
this Jīva-cum-Prakrti ‘body’. In this sense Iśvara is the Field-knower (Kṣetrajña) of the Field
(Kṣetra) constituted of all individual entities sentient and insentient, just as in each individual
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personality the Jīva and the body are the field-knower and the field respectively.
Being in co-ordinate predication (Samānādhikaraṇya), Brahman is an inseparable but mutually
distinct complex of the Prakrti, Jīva and Iśvara. the cosmic mode of body constituted of Prakrti
and Puruṣa is at intervals in alternate states of latency and patency (Pralaya and Sṛṣṭi or dissolution
and manifestation). As the Essence-self of a complex whole, He can be denoted by any of the
terms entering into it—Iśvara, Prakrti or Jīva. Brahman is sometimes mentioned in the Vedas as
Asat (non-existent) when everything is in latency in Pralaya, and as Sat (existent) when all
entities are in manifestations (Sṛṣṭi). All these expressions denote Him only. He is described in
some texts as attributeless. It means only that He is without any undesirable negative qualities. He
is on the other hand endowed with countless auspicious attributes.
Now we are moving to that particualr sloka of Vishnu Sahastrnam
jīvō vinayitāsākṣī mukundōmitavikramaḥ |
here Jivo as I mentioned One who as the Kshetragya or Knower Of the Field
So, It's like Super-Soul(Jiva) & sub-soul(Jiva), Super-soul jiva is only one but sub-soul can be many likes Living-entites,demigods etc etc, So in that particular Sloka the Jiva belongs to Super-Soul which is the knower of the Field.
Now, In your mind this doubt will come if the sub-soul can also knower of the Field So why not he is same level of Bramhan, But here is your dobut clear in this particular sloka of bhagvat Gita which I mentioned before
kṣetrajñaṃ cāpi māṃ viddhi sarva kṣetreṣu bhārata |
kṣetra kṣetrajñayor-jñānaṃ yat tajjñānam mataṃ param || 3 ||
3. And know Me also as the Kṣetrajña in all Fields, O Arjuna. The knowledge of both the Field and its Knower is, in My view, the highest knowledge.
Sub-souls(jiva) are "Field-Knower" of his own body, But the Lord Vishnu(Kirshna) is the ‘Field-Knower’ in all the bodies such as those of gods,humans, animals and antigods.
So, Hope your Doubt clear of your particular sloka that's Jiva refers to the Lord Shriman-narayan who is super-soul, that's jiva is not address to the sub-soul (jiva)
And as In Vishitaadvaita Philosophy
The Visishtadvaita principle is tell us like as we can't discriminate the white color from the white clothes. even though they both are different from each other like same as Davita and Advaita can't be discriminate from each other. even thogh they both are different from each other and same as we and Suprme Lord Visnu are different from each other but also not differentiate from each other.