Food for promotional thought:
Yesterday several prominent E-sports people/gaming personalities live-streamed Kingdoms of Amalur which as far as I can tell was some sponsored thing by the devs/publishers. Stuff was given away (graphics cards, games, shirts, etc) for publicity and people (don't know how many) watched. Gamers that watch those sorts of live-streams are likely heavily interested in the game and/or really like the caster so will give our site some of their weight.
Sponsoring an entire thing like that is probably a bit much, but hopping on the bandwagon seems like a nice idea. Throw in some of our shirts, sponsor some giveaways, buy ads (did they do ads?). That said, I don't know anything about the expense of such a thing, but some more business-y SE person could try to find out.
While this "suffers" in the sense that we're focusing on a single game (as with the tournament question), the benefit is clear; glomming on to a huge publicity swell that pales in comparison to anything else. This gives our site a tremendous push and fair chance (versus competing with existing communities) to get a critical mass for new games, those that will naturally have the most questions.