Games increased my English vocabulary (and even grammar competence) a lot, especially Infocom's text adventures, which had a pretty sophisticated writing style.
My knowledge of certain historical periods, and history in general, has also improved, thanks to strategy games (Civilization, Europa Universalis), and adventure games with a historical setting. Often it's not the game itself that provides the information (though the Civilopedia contains a wealth of information), but the game triggers an interested for reading more about the respective period. Games aren't a very efficient means of teaching historical information (the game itself tends to get in the way of the teaching), but they are uniquely well suited for letting people actually experience a given setting, and/or give them an impression how it _felt_ to live at that time.
There are some abstract skills, like planning/strategizing, which may also have improved due to my gaming habits.