The point has been made by the first chess game - if you think you can hide behind the rules, hoping the enemy is going to respect them, you're a moron. Which was why Lulu still ended up losing to the gangster in Ep1, because Lulu was playing a chess game, and the gangster was playing a game of submission which just happened to include a chess game.
Similarly, the Emperor's Social Darwinism philosophy teaches that morals and social norms such as "mercy" and "justice" are like rules of chess, something to play along with when it suits you and discard when your objectives change.
In this episode, the objective was never "win the chess game" because the chess game was never going to have any impact on the war, as far as Schneizel knew, since he was never going to really give up Suzaku. His objective was to learn what kind of person Zero was.