Yes, but that feature requires the developer to mark that version for it to show up in the "Betas"-tab. Steam doesn't allow arbitrary downgrades to previous versions, only to those made available by the developer. And I don't think it would work here anyway, as it would mean they'd still be selling the music, which they aren't allowed to. This feature is however frequently used when it comes to things like breaking compatibility with older Windows versions or other breaking changes.

When the content removal happens in the process of a larger upgrade, the developers will sometimes make a completely new game entry, previous buyers get both versions and new buyers only the new one, e.g. this happened for some GFWL games.