I think that’s too broad a definition and renders the term near useless (someone who can play an instrument regardless of skill).
In this case I’d regard musician as someone who derives significant portion of their income from making or playing music or at least puts in a significant time into becoming the above (practice, learning and playing).
In this case I’d regard musician as someone who derives significant portion of their income from making or playing music or at least puts in a significant time into becoming the above (practice, learning and playing).