I think it depends on the level of investment being put into the activity - here, listening to music.
I had one friend who was very, very into music. He read music blogs, he knew all the names of all the members of his favorite bands (and there were many), he listened to TONS of current albums, and he went to a lot of shows as well. When he listened to music, I could tell from our conversations that he listened intently and retained a great deal more about a single song from a single listen than I often did after listening to a song several times. I think that was partially because, as a person interested in music, he was listening for and able to hear a lot of finer details that the lay-listener didn't know or care to listen for/hear. I think it was also because he was actively listening, not just passively turning on a track and letting it play while he did other things in the background.
It's like - I hear people talk about "production." "This track was minimally produced and has a very raw sound," or "This track is very produced," or more specifically, talking about styles of production - like Dr. Dre and what makes him a great producer and why.
I can kind of hear production. I can tell when a track is more produced over less. But I am very hard pressed to talk about details of production, or production style, or what it is that makes Dre so great at being a music producer or how he does it. I think people who really care about music and are really good at it, though, listen on a different level and are able to differentiate between things like quality of underlying vocals, quality of the melody/bass line/drum line/etc, and where "production" starts and what it does in a given song.
So I would think someone who writes music reviews would listen to music more on that elevated kind of level, and can see why it could be considered a hobby, because it would be a lot more active than what the average person does.
Then again I see your point, where saying "Listening to music" is a hobby is similar to saying "I like to have fun" when someone asks what you do in your spare time. Well, yes. Everyone likes to have fun. Liking to have fun says little to nothing about a person. It is how they find their fun that is more interesting and important.