When Pete states that if he manages to stalemate the chess game with 12 pieces remaining it still means six people would die (one for each captured piece). Each player starts the game with 16 pieces but two had already been taken so there would be 30 pieces left. That means Pete would have to make a play where both sides would lose 3 more pieces each.
Twin Peaks is famous for numerological references and its possible the 12 pieces remaining with 6 lost is a 666 reference for Windom Earle. Its also noted if both sides lose 3 pieces each that's a 33 reference.
Pete states that if he manages to stalemate the chess game with 12 pieces remaining it still means six people die (one for each captured piece). Each player starts the game with 16 pieces. If Pete is referring to retaining 12 of his own pieces it means four captured pieces, so four deaths, not six. If Pete is referring to 12 pieces overall, that would equate to 20 deaths.