There actually was a time when professional wrestling was real sport, before the worked bullshit took over.
There is a bit of a revival of catch wrestling going on. It's been largely fueled by the success and popularity of certain MMA fighters who are schooled in catch wrestling, like Kazushi Sakuraba and Josh Barnett, among others. This was largely a result of the filtering into MMA of these two, and other fighters, drawn from the ranks of professional wrestlers in Japan, who were schooled in catch wrestling. Many of these guys were trained by Billy Robinson, who was a British legit professional wrestler, who trained at the Snakepit in Wiggin, under Billy Riley, and there is therefore a direct line from the Wiggin style through these competitors.
Legendary American wrestler Dan Gable--for example--also was schooled in catch wrestling as a boy, in Waterloo, Iowa, and small pockets of legit hook-and-shoot wrestling styles have survived here and there, with oldschool trainers continuing to ply their trade quietly beneath the radar. The freestyle wrestling in the first Olympics was catch wrestling, and the sport was practiced by guys like Jack London, among many others of his days. While I am not entirely sure, it seems plausible to me that the wrestling of Abe Lincoln was catch wrestling (or something similar).
There is a fairly small-scale revival of catch wrestling going on currently, with tournaments being held. This is basically attributable to a general revival of popular interest in grappling arts across the board.
I don't think WWE is a sport, although I guess it depends a little on how you define sport. I see it as performance art (and shit performance art). But you could (key word could) say it is a real physical culture, and you might define physical culture as synonymous with sport.
To each their own I guess, but to me WWE embodies the corruption of wrestling. It is likely born of the true corruption of wrestling, through the consequences brought on by the influence of gambling on worked matches. There have been histories produced, but it seems like a somewhat speculative field of analysis.