It's a fascinating theory that, for example, AD&D and B/X are completely different hobbies than 5e.
I doubt you will find much purchase with any theory that requires such limited definitions. IMO.
Maybe not
completely different, depending on how close we look. It's like a fractal -- the closer we zoom, the more distinction we see.
Can we consider gaming a hobby? Sure. Let's look closer.
Can we consider tabletop games a hobby, separate from video games or (I don't know the word) games like football and basketball? Sure. Let's look closer.
Can we consider TTRPGs a hobby, separate from wargames, board games, CCGs and gambling? Sure. Let's look closer.
Can we consider OSR a hobby, separate from New School and Mid School? Sure. Let's...
Yeah, let's stop. I don't really want to type more of the same naughty word.
The huge glaring flaw in your argument is the assumption that these are all mutually exclusive. They aren't. Guess what? Way back in 1981 the "players actively worked together to create a cool and engaging story", and even us grogs now playing 5e play it as the GM being an impartial judge and we use player skill to resolve many challenges.
D&D is D&D. Playing B/X or 5e is all still the same hobby. It's literally the same name of the same type of game. Your flawed analogies of trying to compare collecting firearms with hot wheels is noted.
I didn't say they are mutually exclusive. I did say that they are very different.
If you are running 5E as an impartial judge, you're engaging in a Old School gaming. If you are running B/X with the focus on actively creating a story (and not just getting one from series of rolls), by invoking genre tropes and taking into account story structure (three act structure, five act structure, whatever else you've picked), then, well, you ain't doing it in Old School way.
Yeah, and hip-hop is hip-hop. But no one would argue that cloud rap is very different from old skool. Though, I'd definitely say that "old" and "new" are very stupid terms -- a band that was calling themselves "New School of Russian hip-hop" is now considered
aggressively old-school
And, well, I don't know naughty word about collecting hot wheels or matchboxes... Oh. Damn. Ok. I thought you were comparing matchboxes (like, boxes of matches? I guess someone collects them) to hot wheels. Sorry, disregard that. The only brand of toy cars I know is hot wheels.
Though, continuing with the things I know,
within firearms collecting there are very separate categories. Collecting Wild West guns is very different from collecting WWII guns, which is very different from collecting AKs (no one asked, but this is what I do).