sometimes skilled chess players make illegal moves

Extremely rare. The only time this happened that I'm aware of was quite recent but the players only had a second or 2 remaining on the clock, so time pressure is definitely the reason there

It often happens when the players play blondfold chess, as in this case.

Is this really equivalent to blindfold chess? The LLM has access to the full move history, unlike blindfold chess where memorization is necessary

Even if memorization is not required, you still need to map every move on the board one by one under time pressure, an advance amateur would still make illegal moves.