It's been awhile, but I saved some notes about that:

Overall, Chomsky just didn't seem to grok the contention between him and Harris:

(1) Chomsky got stuck on the idea that Harris was insisting that Chomsky wasn't considering intentions at all, rather than just not considering them properly. This was initially an understandable interpretation of Harris' initial phrasing. As Harris said in postscript:

"I can now see that I was using rather rhetorical language in my book and that Chomsky was entitled to reject my characterization of him on literal (if pedantic) grounds. He had asked the questions I said he hadn’t; I just didn’t like the answers. Conceding this doesn’t render the views he expressed in 9/11 easier to digest."

That being said, Chomsky interpreted Harris' silence as a "refusal to apologize" when it should have been a sign that this wasn't the actual point of contention.

(2) Chomsky seemed to assume that Harris' views were based on trusting spoken intentions. Harris never claimed we should just take people at their word. It was Chomsky who brought up "stated intentions" despite the fact that Harris was talking about actual intentions. Regardless, Chomsky himself had already made assumptions about Clinton's actual intentions that Harris was willing to assume for the sake of argument, so the whole stated intentions premise was a straw man and a red herring to their more fundamental disagreement.

(3) Chomsky repeatedly accused Harris of being an "American-exceptionalist." Considering that Harris started the discussion by acknowledging that the U.S. had many atrocities to apologize for, and even assumed Chomsky's impression of American intentions in Al-Shifa for the sake of argument, Chomsky simply had no business assuming that Harris was "apologizing for atrocities."

(4) Chomsky considered Harris' hypothetical thought experiments "irrelevant."

The core of their disagreement seemed to be couched in the question that was asked towards the end of the discussion. Namely, whether (b)"not caring"(as Chomsky put it) about killing thousands of people was "arguably worse"(as Chomsky put it) than (a)intentionally killing thousands of people.

Aside from just claiming that one was "arguably worse," Chomsky essentially made no actual argument for his position here, as he openly admitted himself- "...and though I didn’t give a definite answer I suggested what I think: that one might argue that on moral grounds, (b) is even more depraved than (a). Again, it seems that you have never even considered [the ranking of (a) and (b)], let alone discussed it."

The thing is, this was precisely what Harris' thought experiment was trying to establish(see 4). Thus it seems that Chomsky spent most of the exchange playing around with straw men(see 1-3), only to wave things off when they finally got close to a point of actual disagreement.