You can easily construct a game board from a sequence of moves by maintaining the game state somewhere. But you can also know where a piece is bases on only its last move. I'm curious what happens if you don't feed it a position, but feed it a sequence of moves including illegal ones but end up at a given valid position. The author mention that LLMs will play differently when the same position is arrived at via different sequences. I'm suggesting to really play with that by putting illegal moves in the sequence.

I doubt it's doing much more than a static analysis of the a board position, or even moving based mostly on just a few recent moves by key pieces.