Definition of musician: a person who writes, sings, or plays music.
If their work is only a recording they can make money off of donations. This is how it works in my example of Hoodie Allen. He was directly telling his fans they could download his album for free and they were still paying for it.
I truly don't see how anything you have said here detracts from what I said.
That's that person you go see at shows, like you know, famous rappers and pop stars and rock stars.
These are professional entertainers.
Beethoven was a musician. So is Aphex Twin. So is a guitar player in a bar cover band. Each have a work output that take very different forms.
Many musicians are composers whose work ONLY exists as a recording.
I don't know how it is possible for you to hold such strong opinions about this topic without understanding these concepts.