Given that much of the gaming community is in the early teens - ages where people still need prompts to improve their writing and reasoning skills, people can gain A LOT from analyzing video games on an online forum. Even analyzing the community (rather than the mathematics of a game) is an excellent prompt for writing skills (much like writing for a school newspaper would be). But it requires a community that respects intelligent conversations over brute-micromanagement ability.
But seriously - among all the methods of having fun that teenagers usually engage in - the video game is the one that has the potential to be one of the most educational (with the exception of pursuing math/physics/programming for its own sake - which you can only motivate very few people towards). Writing and thinking abilities are often the most improved with such forums, because writing requires a prompt, and the online forum is the best prompt for it (it's interesting how much you can write/debate about a RTS game - a debate where people can actually AGREE on something - the rules of the game can be considered as axioms). The only problem, of course, is that it's much easier to waste hours and hours on gameplay than a few hours on game mechanics analysis (or writing/debating about the game). Hell, I know International Olympiad participants from HeavenGames (yes, more than one from that website) who didn't really analyze much the game much (they just played a lot and may have been better off academically if not for such games). So I'm not advocating playing games as most people play them now - I'm just saying that they can utilized in a more educational way if people designed forums that could handle such discussions. Only that it must attract a lot of people - and if those people have a choice between intelligent and non-intelligent threads, most of them will opt for the non-intelligent threads.
So, why write about a computer game when one can write about something more arguably useful? The types of reasoning involved in arguing about the mechanics of a computer game aren't much different from those required in arguing about other logical subjects (seeing that the game world is just a bunch of rule sets - and one must argue "which strategies are best given these rule sets, and given these game conditions"). Mathematics often helps explain which civilizations or strategies produce the optimal amount of resources in a given unit of time. And of course, 12 year olds can receive A LOT of feedback about their writing and behavior. Besides, it's an area where people are more likely to submit something original than an area where people have to re-invent the wheel MANY times, such as most academic subjects.
Of course, I'm somewhat biased, since I'm endlessly thankful for learning about CTY from someone at HeavenGames.
(something that easily could have not happened if I didn't post a "my school sucks - does anyone else's school suck more than mine?" thread there - though specifically, the thread was on a forum of an online gaming clan that sprung off of that website). Most people do tend to hide a lot of their academic accomplishments. Shame for that, because I could have started prepping for math competitions earlier if they were more public about them (considering that the alternatives in school produced NO National Merit Semifinalists or people who cared much about learning). Though that's all an online forum based on a game, not a game. =P It could have easily been otherwise.
Oh, and some links:
http://en.wikipedia.org/wiki/Serious_game http://www.educationarcade.org/ http://www.socialimpactgames.com/