The other thing though is that that is not a simple question. (Edit - the question in the video is: "Can you find something in postmodernism which is not either a triviality cloaked in polysyllables or is false?") It has a trap door built in: the word 'triviality'. If you did find an answer, it would be easy to say it doesn't count because it's trivial. Doubly so because Chomsky already understands a lot of the same things about power and language—he has his own critiques of those, which are not identical with the postmodernists' but there are overlaps for sure—so a lot of that wouldn't strike him as new, just dressed up in pretentiousness. Triply so because if you have the mind of a Chomsky, most things are going to seem trivial anyway.
At a deeper level, Chomsky is an 18th century rationalist, so he's never going to accept a critique of the foundations of Enlightenment reason, and there's no single argument by which such critiques are conducted, let alone a single passage in a text that you can point to and say 'here it is'. Chomsky certainly understands this, so his question is really a bit of theater, a way of cauterizing a topic that he has been asked about incessantly for decades now and must find incredibly boring. He's so polite to the people who interview him, especially to naive questioners, that he doesn't show this directly, but you can see it in the charming way that he can't help but smile a tiny bit when he brings out his perfectly-crafted discussion-ending question. ("So that's about all I can say.")
I think a lot of what he's saying there (and in many other places where he's been asked about this) is more a matter of taste than real disagreement. To someone who values clarity of language and is a master of it, the gobbledygook of the postmodernists (which was mostly a concoction of a small intellectual scene in which people were competing on style) would seem godawful because it is, and would also seem like a huge distraction from things that matter.
I wouldn't want to reread the postmodernists. I did my time in grad school and came to dislike that material because it was so obscure, and because of the emporer's-new-clothes dynamic where everyone felt like they had to pretend to understand it because they were afraid of being the only one who didn't. The primary lesson I gained from that was how to be unafraid to ask a simple question. That's a powerful thing when no one else is willing to.
But what brought me around to respecting them was studying spiritual traditions whose critiques of human concept production are actually much closer to the postmodernists than anybody else. (Edit: I found an old comment where I wrote about this in more detail, if anyone cares: https://news.ycombinator.com/item?id=713432). If you know anything about postmodernism, you know what an irony that is, because the postmodernists made a grand point of rejecting the language of spirit (e.g. presence, awareness, transcendence, anything higher) even more than they rejected the language of rationality. As a result, they end up with nothing. But if you become interested in looking at your own self-deception, nothing is a good thing to have. The conceptual solvents of postmodernism can be useful in that way, and as I said elsewhere in the thread: usually when people reject these things stridently, it's not because of what is wrong in them but because of what is right. (Another example is Freud, which is another story.) I wouldn't put Chomsky in that category though. I think he mostly just finds it uninteresting.