YouTube didn't have much competition when it happened. Twitch is strong, but not as dominant as YouTube was. There exist alternative services (HitBox, Azubu,...).

There wasn't much competition when Twitch.tv spawned from Justin.tv either. However, that's not the point. The point is the majority of the users are entrenched in one service. You can stream from whichever you want, but if the audience keeps going to twitch, you're stuck publishing at twitch.

The majority of Twitch users follow only a few streamers. If the streamers migrate, a substantial portion of their viewers will follow.

Contrast with YouTube: most people view videos from a wide variety of uploaders. If one or two uploaders leave, the viewers will stay where they are.