If a math game isn't entertaining, it must not be a very good game. At their core, games are supposed to provide fun for the players; math games are no different. Good math games hold your attention with entertaining game play, almost making the actual math seem like an afterthought to having fun. You may find it easier to stay focused on learning when the learning is wrapped up in a game.
Games provide new ways to apply the math. The context the game puts the math into helps solidify concepts and rules through actual use instead of simply reading such rules from a book. Playing multiple games based on the same type of math teach you different ways of applying the knowledge since one game's rules may differ from the next game. If you enjoy the math game and play it often, you'll also become more experienced in that area, building up your mathematical capabilities to levels they may not reach without games.
While quality single-player math games exist, some of the best involve multiple players. In a classroom setting, this promotes participation and gives you the chance to get to know classmates better. At home, this could equal quality time with your parents or children while playing the game with them.
Most math requires a firm understanding of a concept but some forms, like multiplication, require heavy memorization. Compared to sitting there with a deck of flash cards and repeatedly going through the cards until you've memorized what you need to know, games make the process more fun. A good math game may even make memorization quicker since you may be compelled to play and memorize more in each sitting.
Motivation may be hard to come by when you're trying to wrap your head around a difficult math concept, especially if you don't consider yourself a math person. Good math games provide motivation, you'll actually want to learn and do math. If you're motivated to learn your math and harbor a positive attitude towards it, you'll probably learn quicker and retain the concepts easier than if you begrudgingly power through a boring assignment to move on to something you enjoy.