In-game music is a unique situation because a game may possess the license to include the music in their game, and you may be granted the right to stream that game, but that doesn’t mean you have the right to stream the music within the game. We know, it’s silly. There’s additional licensing the game would require to give you the right to broadcast the in-game music.
In short, the right to stream in-game music is going to vary for each game. This is pretty much out of the hands of Twitch and more in the hands of game devs. Streamers should review the End User License Agreement (EULA) for the game and look for any mention of broadcast or stream.
The safest option, if you’re unsure, would be turning off in-game music. Some games, like Rebel Galaxy, have included in-game options for disabling copyright music (they’ve also secured in-context rights for a lot of their soundtrack, good job!)
Music for games is generally either created in-house specifically for the game (what is called “first-party content”) or licensed to use in the game by a copyrights holder (or “third-party content”). Some publishers might provide information regarding those licenses and the scope of the agreements between third-party content creators regarding what is or isn’t allowed by end-users (you, the streamer). These would be in the game’s EULA.
Just from the colloquial experiences we have seen from streamers, games with in-game radio, such as Fallout or Grand Theft Audio, do not always have licenses for the music outside of private use of playing the game. Most streamers seem to play by the rule of thumb to turn off in-game radios while streaming.