I think there is a distinction between running as a hobby and running as a sport, even if the sport is technically a hobby too. I mean really, speed is irrelevant to whether or not you're serious about the sport. It's about how much training you're putting in. And if you're putting in high mileage weeks with a good deal of quality, then even if you're not that fast you're probably doing this for something more than a hobby.
The distinction is in what drives you to run and in your training volume. It's not a binary thing, but ignoring its existence is pretty silly.
To the OP, whatever makes you happy, man. Personally I can't imagine not doing a sport competitively. When I tried to half-ass swimming in college (club) I ended up quitting the sport altogether and becoming a competitive runner. So I highly doubt this point is anywhere in my near future, and the thought of just going for leisurely runs without training to get faster actually gives me a little bit of anxiety.