Dark squares are hidden in fog. You only see your own pieces and the squares they can reach. A small amber dot marks a legal move into a square whose contents you can't see.
Ordinary chess pieces and moves, but you only see what's within your vision: your own pieces, plus every square any of them could reach (a sliding piece sees as far as the first piece blocking it). Since you can't see the opponent's moves, there's no check or checkmate — capturing the king directly ends the game. Castling, en passant, and the pawn's double-step are omitted.
Simplification: the AI sees the full board for practical reasons — only the human player experiences the fog.