The reason why Twitch is not going to shut down is because its streams are disproportionately dominated by a handful of PC multiplayer games. Blizzard and Valve aren't going to shut those streams down. Even if they did, the reason why Google is buying Twitch
now is for how the next-gen console launches augmented Twitch's user base, a trend which will persist as the Xbox One and PS4 continue to shatter sales records. Both systems integrate Twitch streaming into their firmware, meaning that unless a publisher disables it, all games released on those platforms have already consented to their games being streamed.
Worst case scenario is we lose things like Twitch Plays Pokemon but I personally doubt it. For the overwhelming vast majority of its uses, it's only going to get bigger.