I think that's a little too specific and doesn't fit a lot of hobbies. People do often make a little money from their hobbies: fixing up and reselling old cars, thrifting and selling on eBay, refinishing furniture, putting up videos on YouTube.
Also, many hobbies have time-critical components. Even all-American pastimes like sports require you to not miss the game.
I'd crystalize it like so: A hobby is something you sink time into where failure has no negative consequences.
Since people like to pick nits here, that probably needs a couple of qualifiers. The sunk time itself can be considered a negative consequence. And the failure may have negative consequences within the hobby — if you accidentally crush your ship in a bottle, you aren't gonna be happy.
But the negative consequences of failure don't bleed out into anything else in your life. You have no need to succeed. That encapsulation of failure is what I think makes hobbies safe and thus encourage fun and a sense of play.
The reason it's so often disastrous to turn your hobby into a job is exactly because of that reason: it means you are now adding real stakes to the game. If you failed frequently and safely when it was a hobby, that was fine and you might still love the hobby. Once those failures matter, it can upend the whole cost/benefit calculation.