I did competition cheerleading (all-star)all through middle and highschool and no, it's not a sport. I did ballet and other dance, that's a sport. I did gymnastics when I was younger, that's a sport. Cheerleading, especially highschool has neither.
The closest thing we got to dance was hiphop, and not even good hiphop. You can never have danced before and win competitions.
Also, tumbling =/= gymnastics. It's = tumbling. Back hand springs, tucks, toe touches, anything else while physically demanding, is not up to what gymnasts do. Competition cheerleading is fairly close to a sport, same way if you consider golf a sport. I still wouldn't equate it with ice skating or swimming or any other solo non-contact sports. Highschool cheerleading is a joke.
Just depends on what you consider a sport to be. But if it is, it's by far the least demanding and skill based sport out.