Whether you call cubing a "sport" or not doesn't change what it is, and it definitely shouldn't change how we view it either.
If you prefer to treat physical exertion as a core component of what makes a "sport" (i.e. you're in the "neither chess nor cubing is a sport" faction), then sure, whatever. Cubing isn't a sport. So what? You can still cube as much as you want, or as little as you want.
If you want to include mental exertion as a component (i.e. you're in the "both chess and cubing are sports" faction), same deal. Now that cubing is a sport… so what?
"Sport" versus "hobby" is a pretty bizarre dichotomy, if you think about it. Reasonable dichotomies would be "sport" versus "not a sport", or "hobby" versus… "thing you begrudgingly do"? Anyway, nothing precludes an activity from simultaneously being a sport and a hobby.
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I pulled a fast one on you. There's a third faction: chess is a sport, but cubing isn't. Per
SportAccord's old website (idk who they are but they try to make themselves look like big shots), a sport cannot involve any element of luck. Obviously, luck is a central component of cubing, so cubing can't be a sport. Case closed!
On the flip side, it's also pretty reasonable to consider cubing more of a sport than chess is. Cubing doesn't require much physical exertion per se, but it's not literally nothing. In chess, you just have to press the clock and move chess pieces around. Unless you're playing in a very fast format (e.g. blitz?), you don't even have to move the pieces all that quickly either. A similarity can be drawn between cubing and any sport where the goal is to do something as fast as possible, or to do as many things as possible within a fixed time limit.
Ultimately, this boils down to how the word "sport" should be defined. As a category shaped by examples (rather than decided by fiat), the boundaries are naturally fuzzy, and cubing (and chess) happen to fall in said fuzzy boundaries. It would be entirely reasonable to treat cubing as a sport, and equally reasonable to treat cubing as not a sport – as long as you have an idea of why you'd consider cubing to be / not be a sport. You could even be noncommittal like I am, because holey sheet
who cares, it's just a word