It's one of the easiest ways for Sims to increase their Logic skill. It also provides Fun, and since two Sims can play, it can fulfill Social needs as well. Children can play, and in Sims 2, will gain Logic skill by playing.
In Sims 1, two Sims playing chess will play a game. If allowed to run its course, it will end when one of them wins. In Sims 2, it appears that two Sims can practice together, but may not be able to play a game which one will win. Even so, mean Sims may attempt to cheat by distracting the other player. If caught, the other player's relationship with the mean Sim will drop.