Twitch is owned by Amazon, so I guess that would be one entry point. GarlandAg2012 had a good idea too about watching the companies that sponsor streams and tournaments.
From what I understand, the tournaments themselves don't necessarily make much money. They're basically just exposure organized directly by the developer to drive player involvement as part of the marketing budget. I know there are starting to be a few cable TV deals here and there, but the most watched games like League of Legends, DOTA, Counterstrike, CoD, Hearthstone, etc., all do free-to-watch tournaments that might recoup costs on ad sales and/or Twitch subs, and actually make money on getting people to play the game. It's like the Nathan's hot dog eating contest - the contest itself probably makes no money, but it does get a lot of regular folks to go buy some hot dogs. Don't take this as necessarily true, it's just my educated guess as to how it probably works from observing for a while. But the real smart play (and the most difficult) might be identifying the next big competitive game and getting in on its studio early.
