I had the same issue with copyrighted music in video games such as some cutscenes in "The Last of Us." Great game but I can't have the video up with the cutscene when the music is playing in the background? It sucks but we don't have the rights to the song unlike the game company that has a license for it. The only solution I find to that is to cut the audio completely during those scenes, play royalty free music and have subtitles on. But you have to have your audio track recorded separately from the game audio track otherwise it won't work.
Whenever I record gameplay-like videos for my channel I cut out all cutscenes to avoid the copyright claims. I figure if people are going to watch it's going to be for our commentary or how we play the game. Not for the story and/or playthrough/walkthrough of said game. Plus it's a lot easier to battle a "content ID claim" if I don't have any of the cinematics in there.