> he discusses using a grammar to restrict to only legal moves
Whether a chess move is legal isn't primarily a question of grammar. It's a question of the board state. "White king to a5" is a perfectly legal move, as long as the white king was next to a5 before the move, and it's white's turn, and there isn't a white piece in a5, and a5 isn't threatened by black. Otherwise it isn't.
"White king to a9" is a move that could be recognized and blocked by a grammar, but how relevant is that?
Whether a chess move is legal isn't primarily a question of grammar. It's a question of the board state. "White king to a5" is a perfectly legal move, as long as the white king was next to a5 before the move, and it's white's turn, and there isn't a white piece in a5, and a5 isn't threatened by black. Otherwise it isn't.
"White king to a9" is a move that could be recognized and blocked by a grammar, but how relevant is that?