This "may" differ from company to company... I'm not sure if that question is maybe a bit above my pay-grade, so I'll do the responsible thing and say "I'm not quite sure. Ask an expert."
The best place to inquire about that without talking to a lawyer is probably the Audio Forum:
https://www.newgrounds.com/bbs/forum/13
Phronemophobia
Depends on the video game theme song and how you recreate it. I've listened to a bunch of old VG covers and remixes here and elsewhere. The problem with them is usually the result of using stuff on the radio that has a major record label attached to it (like the music in a GTA or Fallout). For video games specifically, there's more flexibility since you got people streaming and posting content on YT and it's generally too much of a hassle for developers to strike at transformative work solely due to the music. It is still technically protected, so you would definitely want to credit the composer and ensure that the cover is not being used for profit. If possible, try to get permission from the composer as some will respond. I remember Mazedude commenting on how he was able to reach Tommy Tallarico about using his music from Earthworm Jim 2 to create the remix 'Glow Worm Jim.' - https://www.youtube.com/watch?v=c8MGuGE0sX4
I have found several examples of covers and remixes that are merely created for the fun of it and offered as free to download, as well. Examples on Newgrounds would include HoboKa's remix of FF6's Umaro's theme - "Frosted Rage Flakes" - https://www.newgrounds.com/audio/listen/1112757
...or bertn1991's cover from a decade ago that is simply titled "Monster Party - Title Theme | 2015." - https://www.newgrounds.com/audio/listen/772616
In all likelihood, no one is going to strike your work for a standard recreation of a video game track, BUT the best advice is always the safest - make your own original piece. Still, if one insists upon using a specific song from a specific game, then fiddle with it enough to be distinct from its source material, credit the composer of the original, and do not try to make money off of it.
Note ~ I am not a moderator and there is an audio forum on the BBS if you wish for a more informative response.
Hopefully, you are doing well, feeling well, and not stuck in a well. Well, well, well.