All music is copyrighted, so never ever assumed you're 100% safe. There's always 2 things you do need to be careful of though.
A) Generally an original soundtrack/Original Score/OST (so basically a soundtrack/music/sound effects etc... composed specifically for the title, e.g. Doom, Assassin's Creed, Horizon, Gravity Rush & often many indie games) are unlikely to attract content ID claims or even copyright claims, this is because the publisher/developer retain copyrights & sometimes even distribution rights to the game and that
can sometimes apply to the music in the game as well. Even then, you're much better off contacting the developer/copyright holder, better safe than sorry. I'd suggest it for the game in general.
B) A soundtrack (so soundtracks that use a collection of 3rd party music, e.g. GTA, Watch Dogs, Forza, Sleeping Dogs, Need For Speed) are very likely to attract content ID claims or even copyright claims. Generally I turn off music altogether in games like these.
If you're ever in doubt for any specific title, just contact the copyright holder. Fair use doesn't apply to music in the same way that it does to games.
I have also seen lots of videos where people have used soundtracks and just put in the description 'In Game Music' and seem to have no copyright issues.
Putting things like "copyright infringement not intended" in the description is about as useful as a cold blooded murderer telling the judge they didn't intend to kill their victim and getting released completely free of conviction. It does not work & if they're getting away with it, either they're featuring games that fit in category A). Or they're getting lucky, it's usually the latter.
ke I said most of them you won't get in trouble I'm a gaming YouTuber and all the videos I've recorded & uploaded I've had no issues with.
That's because literally every game you've uploaded a video of so far, has had music specifically composed for it, bar GMod. A lot of indie titles are good like that, they usually can't afford to pay royalties to large artists or record labels. Little guys helping little guys I say.
Best thing I can suggest when contacting developers for permission and asking if you can use their games; is to specifically ask to use
both visual & audio content from games they own the copyrights to. You can literally word it like that too or: "
I would like to know if INSERTPUBLISHERNAME would allow me to produce transformative works (Previews, Let's Plays, Reviews etc.) using both visual & audio content from games you own the copyrights to?" (I actually got that from AlloySeven's template). They will actually tell you if the music is not theirs and even tell you if there's titles they don't own the distribution rights to. I think the devs of Shadowrun told me they didn't own the rights to Shadowrun but Microsoft did, so I had to go by Microsoft's policy on publishing & monetization.