I've played tournament chess for a few years. In fact, I'll be playing in a chess tournament this weekend. I've lost lot of games. The effect, I think, has been an increased ability to handle failure, rejection, and frustration in other areas of life. How one gets better at chess is a subject of intense interest among chess players. Of course, one has to learn opening principles, positional ideas, endgame technique, tactics, and more. However, I think there is also a psychological change that must happen. A transformation in how one views the game. Generally, I think it happens this way. A tournament player eventually realizes that the game is (most likely) a theoretical draw. Nobody can win a game by force. Every loss is the result of your own mistakes. Coming to that realization the chess player stops trying to force wins from unclear positions, stops mentally calculating long and wild variations that eat up time on the clock, and in truth will never appear on the board (and are full of errors anyway), and instead begins to focus on his opponents (perhaps subtle) errors. He begins to accumulate small advantages. In short, he lets the other player beat himself. Of course, it's all easier said than done.
