It's much, much harder to exert copyright on live content, in contrast to YouTube's ContentID system.

Twitch has taken down streams of unreleased games (which is fair because Twitch makes this rule very explicit), but that's still on an ad hoc basis.

Don't see a YouTube ownership changing that, I assume it'll still be about live streaming.

Large companies tend to err on the side of taking down more than they legally "have to". I know of YouTube videos that were taken down because of copyright claims that were outright false (that is, the entity making the claim didn't even have any rights to the material that was allegedly being infringed). There's a lot of room to be more lenient than YT and still on the right side of the law.