Twitch is not interactive so it can just buffer for a few seconds more and handle the typical worst case of TCP. It'd probably still be better over UDP but I'm not qualified to say that for sure. I'm sure the twitch.tv guys could chime in on their choice and inform us of the pros and cons for their situation. The correct choice is application specific.
Not necessarily. One of the largest live video streaming services, Twitch.tv, uses TCP for streaming.