While Nintendo won't put a copyright strike on your channel and take the video down, they may put a copyright claim on the video and will take any ad revenue the video generates.
If you are a smaller channel that cannot monetize, then there really is no harm as you wouldn't make money either way.
The fact that Nintendo is using open source music in the game, I don't really know if they can claim their take on it as it's open source, so you may be ok.
Worst-case scenario, Nintendo puts a claim on the video. I don't think anything worse can happen. Either way, the video will be viewable.
EDIT: I was thinking "Wii Music", but if you mean Wii system music, then there is a higher chance of them putting a claim on the video, but I still don't think that they will take it down because of it.