Under US copyright law, anyone may make a "cover recording" of a musical work (such as a song) that is not part of a drama (such as an opera or musical comedy). The would-be cover artist can either negotiate for permission and a royalty rate, or use a compulsory license, known as a "mechanical license", at a royalty rate fixed by law. The right to do this is given by 17 USC 115. However that section of the copyright law is rather complex and confusing. The Nolo press explanation of cover rights says:
To record a song for release to the public, a performer must obtain permission from the music publisher of the song and pay a fee, called a mechanical royalty. A mechanical royalty must be paid when songs are reproduced, for example on compact discs or records.
There are two ways to get permission and pay the mechanical royalty:
- A compulsory license may be used, and the preset statutory mechanical royalty rate paid directly to the music publisher—the easiest, least stressful method.
- Permission and a mechanical royalty may be negotiated directly with the music publisher or the Harry Fox Agency.
Under the compulsory license procedures, you need not ask the music publisher's permission to make the recording or negotiate a license fee. Instead, you merely inform the publisher of the recording and pay a license fee set by law.
You can get helpful information about the procedure by downloading Circular 50, Copyright Registration for Musical Compositions, from the U.S. Copyright Office.
When using the compulsory license procedure, the music publisher must be paid a mechanical royalty rate set by the government—sometimes known as the statutory rate.
There are additional restrictions. A mechanical license is not available unless the4 copyright owner has previously made or authorized a recording of the work and released it for distribution. A mechanical license is only available for the purpose of creating and distributing copied for individual use, not for broadcast.
However, as explained in this Soundfly article if the musical work is presented along with any visual content, such as a video, a "synchronization license" is also needed. This would very likely apply to a video game. As Soundfly says:
Typically, in order to acquire a sync license, you just need to ask the publisher. Unfortunately, there are no set prices for this kind of thing – we don’t even have a pricing scale available! Sometimes you can get it for free, and other times it’s going to cost you dearly. Hopefully, it won’t be the latter.
This is not covered by the compulsory (mechanical) license, and must be obtained via negotiation. That means the would-be user must find out who the copyright holder is first.
By the way, the compulsory license is called "mechanical" because this provision was originally passed to permit making rolls for player pianos, which reproduced notes mechanically.
In short, both a cover license and a sync license are needed, and the second must be negotiated.
See also this Wikipedia article.