If I had a hope of being a professional DotA player, maybe the distinction would not be as clear.
I like to look at things as training skills (see my 10-100-10k model, [0], nicely improved by noahl). If you never played DotA before and sit on it for a dozen hours of so, you'll be familiar enough with it to decide whether to continue deliberately training it to get better, just play it casually for fun, or drop it altogether. The first implies that you have a goal, so I'd classify this as productive (towards that goal, maybe you really want to be on top of a local ladder, or whatever it is in DotA; I don't play it). The second means that it's just recreation for you, and it's fair to classify it as such. We all need to do something for leisure, one man plays football, another plays guitar, yet another plays StarCraft.
In other words, I classify things as something I either deliberately want to get better at (thus doing it is productive), or do just for fun without caring about improving the skill (thus this is doing things for fun). Both ways of spending time are good, but it helps to be clear about which is which.
Similarly, for photography, it frustrates me that I can browse the top page on 500px and see thousands of photos per hour that I can never hope to match even once. Still, I do it because I like it. I don't think I've ever done anything just because I want to get good at it, and I've been programming most of the day for 20 years, because it's fun for me.
All in all, there's a spectrum of the metrics you mention, I don't think it's discrete.
I agree. I simplified it to two different categories for the sake of the comment, but it's better to think of it as a spectrum.
After some hours of photography, you have some photos which did not exist previously. After hours of DotA you have only some improved muscle memory and so on, nothing tangible.
This heuristic would however rule out the learning of more "worthy" pure skills, jazz piano, unicycling etc.
I don't think I can formalize it easily, sadly. I guess I hate Dota because I play it even though it frustrates me most of the time, and it doesn't leave me with any lasting skill other than itself.
To me, creative skills are not inherently meaningful until practiced. Except I suppose for improving ones self-image as a "creative person," which is ultimately a self-destructive pursuit.
If one goes around "being a maker" without actually making, that distinction exists only within ones head. Seems pretty solipsistic.
Photography, for me, is similar. I take photos because I like the process and the output, not specifically so other people can see them. There's a tradeoff there, but I'm not sure I could say that playing basketball is useless, for example (although that has more health benefits than Dota).
It's a hard question. Similarly, learning a foreign language feels very useful to me, even though it doesn't produce anything at all.