At around 1:07:00 he's asked if his view is Prasangika. He clarifies that is it more how Tsongkapa reads Chandrakirti, also distinguished in the Batchelor thread with how Gorampa sees Prasangika. Hence the two truths debate elaborated therein. Thompson is using the distinction between Yogacara and Madhyamaka, and the Batchelor thread shows the heavy influence of Yogacara in the Gorampa versions of Prasangika Madhyamaka.
Around 1:21:15 he is asked about the narrative self. He responds that it is doesn't have to be seen as an fixed substance with independent existence or substance (1:23:30). Which reiterates previous points above that the narrative self through language is not necessarily an illusion divorced from our pre-linguistic or core self but can be an extension of it.
Another point Thompson made in the last post was that the narrative self can go to far and get disconnected from the core self. Which reminded me of this post by Thakchoe on conceptual elaboration, which in itself is beneficial and has a place in the transcendental. It is only when it becomes 'proliferation' that it is a problem.
From the Lingam video at the link, speaking of Nagarjuna's teaching:
"The idea being to clear the mind of any and all concepts about reality so that reality itself could be directly experienced" (5:20).
Recall this from Batchelor:
"As soon as the seductive notion of 'truth' begins to permeate the discourse of the dharma, the pragmatic emphasis of the teaching risks being replaced by speculative metaphysics, and awakening comes to be seen as achieving an inner state of mind that somehow accords with an objective metaphysical 'reality'" (92).
Immediately following Kennilingam goes on to say that every branch of Mahayana agreed with the last above statement. (Wrong, see the Batchelor thread.) And he then admits that the third turning was Yogacara, which also is in agreement with that statement. That is true, but again it is a continuation of a of metaphysics of presence, not at all the kind of postmetaphysics Batchelor talks about. Or Nagarjuna of Tsongkhapa, for that matter. At 7:00 he notes it's time for the fourth turning, and with that I'll agree. But it's Batchelor's sort of postmetaphysical turning, not the metaphysical rehash he's talking about in the above quote that he apparently wants to retain.