> There is no legitimate reason to make an illegal move in chess though?

If you make an illegal move and the opponent doesn't notice it, you gain a significant advantage. LLMs just have David Sirlin's "Playing to Win" as part of their training data.

You raise an interesting point. If the filtered out illegal moves were disadvantageous, it could be that if the model had been allowed to make any moves it wanted it would have played to a much worse level than it did.