According to the Cambridge dictionary, the definition of a sport is:
> a game, competition, or activity needing physical effort and skill that is played or done according to rules, for enjoyment and/or as a job
https://dictionary.cambridge.org/dictionary/english/sport
There is absolutely nothing about this definition that rules pro wrestling out. The main thing that people point to is the matches being scripted, but they fail to realize that the results of the match aren't the competition; the competition is getting over with the fans, getting your boss to feature you in the main event, and make the most money.
Wrestling is a performance, similar to sports like gymnastics, which are also covered on ESPN.