Twitch, unlike YouTube, has a ton of experience dealing with gamers. They have direct contact with their streamers, organize events (TwitchCon, esports events etc). The Amazon acquisition has been incredible to twitch so far, too. The Amazon Prime/Twitch Prime promotion has gotten streamers a ton of income and has been overwhelmingly welcomed by the twitch community.

YouTube, in the mean time, has a broken DMCA/content-id/copyright claim system - a constant source of complaints with no support channel to actually help.

I find it fascinating how, in YouTube competition, where Vimeo and DailyMotion are failing, Twitch is succeeding because they are simply focused on their strength and advantage, rather than try to just provide the same service with a nonexistant community. And now with Amazon behind them, they have the money to double down on it.