You're missing the _hard work_ part. Sure there's always an element of "luck" in any story of success, but that mostly has to do with timing, and is much less weighted than the perseverance and hard work of the people building it.
Twitch is a full-featured, very mature application with many moving parts outside of just the video streaming, and building all those parts took an incredible amount of time and effort.
Twitch is a full-featured, very mature application with many moving parts outside of just the video streaming, and building all those parts took an incredible amount of time and effort.