So not Netflix, but Twitch?

Plenty of people stream commentary to matches without showing the game itself, so that would flag as guilty too

These are not peer to peer connections. These people would send a single stream to twitch and then twitch, a known streaming service, would stream it to their viewers.

In theory someone might rent a server and do the streaming directly to his viewers, without using a known platform. This would be a legitimate false positive as you describe. But this would be so expensive I doubt anyone would do it when the alternative is a free platform with built in community and monetisation tools.