The Twitch logo was designed by a graphic designer called Kiko, who was working for the company at the time. The logo was designed with a silhouette of a boxer in mind. The idea was that the design would turn into a silhouette when inverted.
The logo was designed before the company even had a name. The company was called Twitch Interactive at the time and they used the logo as a way to get the attention of the public.
The company wanted to move away from the idea of being just a gaming-based channel and focus on becoming a place where people would come to watch and share videos and livestreams. The logo needed to reflect the new direction that the company was taking.
They wanted a logo that was simple and that could be easily turned into a silhouette. They also wanted to reflect the idea of motion in the logo, hence the diagonal lines. The logo was also designed to look good in black, white, and red.