saṃhataparārthatvāt triguṇādiviparyayād adhiṣṭhānāt |
puruṣo ‘sti bhoktṛbhāvāt kaivalyārthapravṛtteś ca ||

Since the assemblage of sensible objects is for another’s use; since the converse of that which has the three qualities with other properties (before mentioned) must exist; since there must be superintendencel since there must be one to enjoy, since there is a tendency to abstraction; therefore soul is. (Colebrook’s edition and translation)

Veṅkaṭanātha first focuses on the first logical reason (“since the assemblage is for another’s use”) and contexts it with some counter-arguments:

sāṅkhyādyuktāny anumānāni tv asādhakatamāni. paṭhanti hi saṅghātaparārthatvād iti. atrādye patyādiśarīrārthair bhāryādiśarīrais siddhasādhanatā. na ca tāvad atiriktaṃ khaṭvādidṛṣṭānte ‘pi dṛṣṭam.
anavasthābhayāt tasyāsaṃhatatvakalpanād
[…]
varaṃ śarīrasyānanyārthatvakalpanam | (SĀS ad TMK 2.2).

The inferences [about the self] said by Sāṅkhya and similar schools do not prove [their point]. In fact, they recite that “[the self is different than the natura naturans] because a complex (like that of body, sense-organs, etc.) is for the sake of something else” (SK 17). In this [kārikā], the first [logical reason] establishes something already established, since, for instance, the body of a servant is for the sake of the body of her master. Nor, to begin with, is this an isolated [case]; it is seen also in the example of couches and other (pieces of furniture) [which are for the sake of someone else]. (Thus, even if it is true that complex entities are for the sake of something else, this does not prove that the natura naturans is for the sake of precisely the self.) […] It would be better to postulate that the body has no other purpose (apart from serving the self).

What is exactly the point here? In my opinion, Vedānta Deśika says that showing that being complex is being for something else is a well known thing, and that this does not prove that it is for the sake of the ātman, which should have been the purpose of the kārikā.