Competitive Dance / Cheerleading, like gymnastics, diving, and so forth, is adjudicated athletic exhibition.

Nothing inherently wrong with that.

But whether that is a sport really boils down to semantics.

"A sport," to some, must include a minimum threshold for athletic activity
AND

a clear method of determining a victor based on meeting the objective(s) of the activity in direct competition with other entrant(s). Most points, fewest strokes, fastest time, longest distance - all measurables.

To some, only one of the two is required (though, the people who think an activity can be considered a sport with only the second above condition can go suck rocks. Competitive video gaming is not a sport, and people who think it is are, well, I'll keep this G rated and not continue that sentence).

Most activities that meet the above two conditions can accurately be described as "games." But even then, ambiguity creeps in.

What about archery or shooting? Firstly, despite the fact that there's no debate those activities require skill, there isn't consensus on whether the amount of athletic exertion it requires qualifies it as an athletic competition. We can clearly see that those activities are more athletic than board games, video games, or even darts (which is conceptually the same). But for some reason, the different forms of competitive shooting aren't often considered a "game," in the way golf or darts are.

(And, as an aside, considering the above example, it's humorous that in the English language, both the terms sport and game actually derived from shooting/hunting activities, which are often considered neither in the modern definition.)

So, if your definition of sport excludes judgment as the method of determining victory, you're cutting out some of the most impressive athletic events in humanity.

I don't mind calling Gymnastics a sport, but if clarification is required, I also don't mind referring to it as a "judged sport." ...which basically just allows us a reason to believe "our" entrant got hosed when they didn't win.