To state the bleeding obvious, Twitch's software and infrastructure isn't worth a billion dollars. The owner of YouTube could have made a strong expansion into game-centered live streaming for a tenth of that figure, most of the work focused around creating the right user experience for streamers and viewers, and making a few deals to broadcast key events and personalities.
And then we would have two strong players in the market competing with each other, forcing each other to improve. Twitch would have the established pool of streamers and viewers, the deals with console-makers, the first-mover advantage and the indie cred. YouTube would have the rock-solid infrastructure, deep pockets to expand their reach, and the billions of eyeballs that are already visiting their site to watch cats doing funny stuff.
Instead, with a billion dollars, Google buys itself a lock-hold on an exciting emerging market. Their presence will actively dissuade anyone new from making a serious bid to join in, because who has the resources to go against Google when they have bought themselves such a massive head-start?
It's a deal that makes perfect sense for both parties, but the consumers lose.