Up to fair use. There's a good argument that streaming a game is fair use. It's highly transformative, not a market substitute, contains criticism/critique/commentary on the original, and contains only a fraction of the game. That's hitting all four of the factors considered to at least some extent [0].
Reuploading someones stream exactly, no way in hell is that fair use. It's not substantially transformative, it is a market substitute, it is for profit (as is the original stream) and it doesn't contain any added commentary or criticism, it might be only a fraction of the stream, but that's one factor out of four at best.
[0] https://en.wikipedia.org/wiki/Fair_use#U.S._fair_use_factors
IANAL
This is a very US-centric perspective. For example, in Germany's Urheberrecht, there exists no concept of fair use.
I can see that if you organized game-streaming as an entertainment provided by a company, that company would most likely want to hire an editor to provide a best-of version.
(That's essentially how all those reality TV shows like Big Brother worked. Plus some extra dramatization, of course.)
There's economic value to consumers in getting the best-of version, so I am hoping that the participants will find a way to share the larger cake.
So the publishers own the game, the streamer owns the performance, and the reuploader owns the edit. In theory each requires permission from the previous (including transitive relationships, so the reuploader requires permission from the publisher since the edited version still contains content from the game).