The main thing about Sanskrit philosophical commentaries is that they are the standard way of doing philosophy. For centuries, they were almost the only way of doing philosophy. After Maṇḍana, one starts seeing monographs dedicated to a specific topic. Still, even those take often the form of verses+autocommentary and do not become the mainstream form of philosophy. Until today, Sanskrit philosophers think and write in the form of commentaries. This has several implications:

1. They do not value originality per se. I am probably preaching to the converted if I say that one can make incredible innovations while writing a commentary (and in fact, this routinely happened, with sources of knowledge being removed from the list, new accounts being added, completely different explanations being offered etc.). However, the genre “commentary” involves the habitus of intellectual humbleness. One does not praise one’s innovations and rather locates them in a tradition of exegesis of truths that were already available for everyone, if only one had paused long enough to see them.

2. Lower level explanations about word-meanings, sentence-syntax etc. are mixed with high level elaborations. This means that even the most self-confident intellectual will not disdain intellectual labour, because the two are contiguous.

3. Philosophy is constantly seen as a dialogue with one’s intellectual predecessors. In fact, and unlike in other philosophical traditions, Sanskrit commentaries typically take the form of dialogues among possible interpretations.

4. The constraints of the commentary open the way for the never-ending play of possible interpretations. Abhinavagupta lists 18 (if I remember correctly) interpretations for the word anuttara in his Paratriṃśikāvivaraṇa and everyone is aware of the amplifying potential of commenting on words and texts.

In later times, I would add two further features of commentaries:

5. Commentaries tend to take into account more and more networks of texts rather than single texts

6. Consequently, one comments not only on the texts of one’s schools, but also on influential texts one wants to appropriate (think of Śaṅkara’s inaugurating the use of commenting on the BhG and the Upaniṣads, as well as Abhinavagupta’s commentary on the Triṃśikā). Still later, one comments on the texts on one’s adversaries as a way to refute them, like Madhusādana Sarasvatī did in the case of Vyāsatīrtha.

UPDATE: I am sitting in a workshop about commentaries and Ash Geissinger points to something similar to No. 2 in Arabic commentaries to the Quran, and Y.K. Lo to something similar to No. 3 in Chinese commentaries.