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Excellent question. I think it does but it depends on the game. For example, if you're playing a game like Naruto where you're fighting one on one, then peripheral vision isn't really taxed and as such, isn't really trained. You just have one person to focus on. But if you're playing a game like Call Of Duty, where you have to run around, watch your map, hunt foes, and watch your entire environment for the slightest movement, then you are definitely training your peripheral vision. In DC comics, Death stroke once said that playing first person shooter games helps him practice his aim and observe his surroundings. So I guess we can say that the writers have an idea of the effects of gaming on vision.
Not only does gaming improve peripheral vision but it also improves hand-eye coordination. So in essence, gaming is actually good for you, if these two things are what you're looking for.