DotA is a competitive game, and if you compare yourself to other players, you're chasing a moving goalpost while your returns are diminishing. It would be the same if you were measuring your photography skills by one-upping other photographers on a some kind of daily amateur photography tournament.
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.
I don't think it's as clear as that. I want to get good enough to win Dota most of the time, but the global matchmaking means that I only win 50% of games, and enjoy only a percentage of those.
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 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.
[0] - https://news.ycombinator.com/item?id=8197334