Not necessarily. As a counterexample, people (many of whom are very creative and talented) put staggering amounts of time and dedication into playing and becoming skilled at video games for no reason other than personal entertainment. Videos of people playing games are freely available and no profit is typically expected.
A similar phenomenon might be observed with music, where players of music dedicate large amounts of time to playing music and upload the fruits of their efforts to the internet for the enjoyment of their peers.
The cases you're describing either involve someone who spends some other portion of their time (probably "full-time") on money making activities, or someone who has an external means of support (trust fund, savings, fortune they earned earlier, family, whatever).
In the former case it's pretty much as I originally described. Sure, if they're dedicated and don't have any other time sinks like a family, you may still get some music from them, but significantly less or lower quality music than you'd get from them if they could spend full-time on it.
In the latter case.... it's true enough that people in this position have the privilege of studying and creating music full-time without any expectation of payment. They have all the money they need, they're free to spend their time as they wish. Of course, saying this is our economic model means that most of our music has to come from people in this position, mostly kids, retirees, and those with rich family or other benefactors.
And depending on your tolerance for how undemocratic that's likely to be, maybe that's OK. Though I think that if one accepts a picture of the world painted in the article where an increasing number of people aren't even needed by any of our market, civic, or social institutions, the prospect of having them also sidelined in music and other letters gets a little more troublesome.
(And as another tangent: while I enjoy video games myself -- even some very difficult ones that require big investments of skill -- I'd be very careful about drawing larger lessons about skills from them. One of the reasons we enjoy these games is that their practice-reward cycles are often significantly shorter than many comparable real-world skills.)
A similar phenomenon might be observed with music, where players of music dedicate large amounts of time to playing music and upload the fruits of their efforts to the internet for the enjoyment of their peers.