Any game music is technically copyrighted, but more often than not game companies allow in house music to be monetized for that game related reviews/play throughs. However not all companies do this, and some will outright block the video or monetize it for themselves (like nintendo). In this case since you want to use very old music from that era of games it's more likely than not that the music isn't entered in the copyright system as the game companies who made those games 20 years ago are no longer in existence and no one holds the rights to the games at the given time. However nintendos first party games are more than certain in there and will get matched. For example:
youtube.com/watch?v=VH8mQRXemuo
If you right click on the white space and view source (in chrome at least), scroll to around line 100 or ctrl+f it and look for " <meta name=attribution content=".
In this case that line is
<meta name=attribution content=Nintendo_audio/>
meaning nintendo content id snes/nes mario music.
This works for any video. If you can't find that line then the music hadn't been content id (and is attributed to the user who uploaded it or his network). Keep in mind that just because a song isnt in the content id system now doesnt mean it cant get added later by the parent company.