I'm not a lawyer and this isn't legal advise. I don't think that it would be a breach of trademark if you sponsor an event but the event itself may well need a commercial/cyber cafe license for the games that they plan to use in the Tourney - you might want to make sure that is all in order before putting your name to the event.

There is also the issue of "right be damned". Some companies may not want you using their game in this way and may threaten or actually take action against you regardless of if they are in the right of not. Bigger companies have packs of lawyers who are fed on nothing but raw meat. They have to pay them anyway so they may set them on you just to dissuade you.

In any event - talk to a lawyer - see List of Game Industry lawyers.