Twitch streamers do that because they are streaming GPU intensive workload (video game) that would compete with streaming software for GPU resources.

It also prevents driver crash caused by a video game to crash a stream.

Additionally, running on a different computer allows for eg adjusting scenes in OBS or moderating Twitch, without losing focus from the running app/game.

Yeah that makes sense. I was thinking that the two computer setup was also something they did to keep their streaming stuff completely separate from the rest of their life, to not accidentally doxx themselves on-stream and to not accidentally execute malware on the same host they do their email and banking etc on.