Chess isn't really Morse's game. He knows the rules and basic strategy. Doubtless WPC Trewlove could trounce him on the chessboard. His best game is one which is played in the real world against a killer. This match is over: the queen saved, the opponent defeated. There will be others.
He's been forced to play another game: politics. The sly, unseen opponent is ruthless. Thursday urges him to take the safe way out. He won't, no matter how often he's put into check. It may yet end in mate, but he'll be damned to hell before he'll resign this game.