If I found a video with a remake/remix/version of a commercial song (for example, the theme of Super Mario Bros) with a CC BY licence, I can take this video for a commercial purpose like the background music of my game?
Insert I-am-not-a-lawyer disclaimer here
The notes of a song are already eligible for copyright. Taking the notes of a song and interpreting them differently creates a derivate work. This work must not be published when the copyright holder of the original song didn't give their permission.
When the composition of the song is not under a free license, the one who made a remix licensed as CC-BY likely already committed a copyright violation. The CC-BY license in this case is irrelevant, because they didn't had the right to publish the work under any license in the first place. When you reuse their work, you are also committing a copyright violation. Not against them but against the original IP holder (in this case Nintendo).
Such copyright trojan horses can not just slumber in the composition. Other parts of the work can also violate other peoples copyrights. Individual instrument or voice samples, for example.
What do we learn from that? Never trust allegedly free assets. When you want to publish a game, you should get a written contract from everyone who made your assets stating that they have the full copyright on the assets and that they will reimburse you for any 3rd party claims when it turns out that they have not. They will likely not be willing to give you that warranty for free, so you will have to pay them.