This is
murky murky murky. Copyright and "fair use" is complicated enough... this even more so.
First off...
we advise our partners against monetizing GTA. This is because of the movie / cinematic scenes which the game relies on. Those are not allowed. (for Creator X anyway)
From your post... it seems this is popular music, right? (as in, songs that would normally be on the radio or released by artists) You do indeed have additional considerations there. Regardless, whatever type of music/sounds... the gaming company has the rights to use it via creation, commission with full ownership, or licensing.
However, that doesn't mean they can or do pass on any rights to you!
If it's their creation or they own all rights, then the allowed usage is "fair use" or most likely, but not guaranteed to be, whatever fits in their existing policies for using the game itself.
If it's popular music or otherwise licensed, then the most likely scenario is that the gaming company
only licensed it for usage in the game, so you can't rely on any kind of protection there and instead fall back to trying to determine what is "fair use".
Bottom line: You're only protections for gaming videos and the sounds within are "fair use" (which is hard to determine) or use within terms of the rights holders... whether that is the gaming company, the sound production or music company, or a
gaming network that works that stuff out themselves (permission/licensing) and can advise you.
We would advise to at least turn off the music if possible.
Hope that helps!