One of the controlling metaphors in The Killing Game is the idea that life is a game.
Dom is engaged in what for him is an exciting and pleasurable hobby though at the beginning of the novel he is suffering from ennui because killing people is losing its panache. He decides to kill Eve Duncan because she is tough, intelligent and challenging, and he constructs an elaborate game to wring all the pleasure he can get out of it.
His game consists of rather sadistic psycho logical torture in choosing a young street kid, Jane, who distantly resembles Eve's dead child, as a victim. He intends for Eve to bond with Jane and try to protect her.
Then he will kill Jane, so he can enjoy Eve's torment at losing a second child.....