My opinion is pretty much the same as Idolo's. It's not a sport. A sport is defined as: "an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment."
Is there physical exertion? No doubt. The keyword is "compete" though. A staged event involves no genuine competition. That's the difference between a sport like boxing and WWE. It makes me think of a debate I watched about whether "visual novels" should be regarded as video games. I know it's a different topic, but the principle is generally the same. A game is not a game unless there is an objective and a sport is a kind of game. Sports have objectives: beat the opposition. A game can go either way however based on multiple factors, but obviously it usually boils down to skill. If you're playing a part and following a script, like with a novel there is only one outcome.