The song is distinct from an artists performance of that song, but let’s move outside of music to books etc.

Suppose A creates an epic poem, B does a poetry reading aka a performance of A’s poem. C plays that recording back in public. D reinterprets the poem making a new public performance. B can successfully sue C but not necessarily D if it’s sufficiently distinct. A however can potentially sue D, C, and B if none of them got the rights.

This is why JK Rawling got paid by the people making Harry Potter movies, she could sue if they didn’t pay. Trademarks may also be involved, but even without that if you want to make an MMORPG based on The Dresden Files or whatever be prepared to fork over cash. Unless you follow the Disney approach and use public domain works.