"Most striking" in the sense of "most obviously not ever even remotely legal," yeah.

But the most interesting and thought-provoking one in there is [1] Carlsen v Inarkiev (2017). Carlsen puts Inarkiev in check. Inarkiev, instead of making a legal move to escape check, does something else. Carlsen then replies to that move. Inarkiev challenges: Carlsen's move was illegal, because the only legal "move" at that point in the game was to flag down an arbiter and claim victory, which Carlsen didn't!

[1] - https://www.youtube.com/watch?v=m5WVJu154F0&t=7m52s

The tournament rules at the time, apparently, fully covered the situation where the game state is legal but the move is illegal. They didn't cover the situation where the game state was actually illegal to begin with. I'm not a chess person, but it sounds like the tournament rules may have been amended after this incident to clarify what should happen in this kind of situation. (And Carlsen was still declared the winner of this game, after all.)

LLM-wise, you could spin this to say that the "rational grandmaster" is as fictional as the "rational consumer": Carlsen, from an actually invalid game state, played "a move that may or may not be illegal just because it sounds kinda “chessy”," as zoky commented below that an LLM would have done. He responded to the gestalt (king in check, move the king) rather than to the details (actually this board position is impossible, I should enter a special case).

OTOH, the real explanation could be that Carlsen was just looking ahead: surely he knew that after his last move, Inarkiev's only legal moves were harmless to him (or fatalistically bad for him? Rxb7 seems like Inarkiev's correct reply, doesn't it? Again I'm not a chess person) and so he could focus elsewhere on the board. He merely happened not to double-check that Inarkiev had actually played one of the legal continuations he'd already enumerated in his head. But in a game played by the rules, he shouldn't have to double-check that — it is already guaranteed by the rules!

Anyway, that's why Carlsen v Inarkiev struck me as the most thought-provoking illegal move, from a computer programmer's perspective.