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