Sure. It’s more cosplay than sport.
Not that carrying brooms around is an aesthetic match for flying.
If they were serious about attempting an analogue for the feel of the game, rather than the dress-up, it would have to be something much faster than that. Jet skis, maybe; this adds the factor that getting knocked off your ride is inconvenient.
How many fictional games actually work as games? Probably not many. And how many of them are actually good games? Is there one? The talent to write a book, or any other version of storytelling for that matter, seems to be very different from the talent to create good games (giving me a little bit of sympathy for JK Rowling).
Lightning bolt! Lightning bolt! Lightning bolt!
ETA: Dammit! There are times when it’s appropriate to have all caps! Damn stupid board software…
Am I getting drunk yet?
How about games that are fictional even with the context of the work of fiction? Mark Harris’ Henry Wiggen quartet (best known book: Bang the Drum Slowly) had the baseball team constantly drawing suckers into their card games of Tegwar. Like Mornington Crescent or ST:TOS’s Fizbin, it was made up on the spot - the name stood for The Exciting Game Without Any Rules.
Well, I wouldn’t say more, but yeah, cosplay is certainly an element.
Well yeah, but it’s difficult to come up with an analog. They’re brooms, because wizards use brooms, and it’s ultimately about the source material. We just don’t have flying brooms, so have to make do. Just like the snitch isn’t a self-propelled ball the size of a ping-pong ball - how do you make a crafty, self-propelled ball? Answer: cheat, tie it to a human.
Well, you’re trading off. I mean, segways make sense for a closer feel, or you could use mini-motorcycles for that matter, but the risk factor goes up as well, and we don’t live in a world with magical cure-alls. This is Intermural flag football for geeks, dressed up in Potter clothes (the game, not just the players). If you wanted to make an NFL league version, sure, you could up the ante with equipment and appropriate safety gear. Give it a couple decades, maybe they will. 
This comment made me recall that this weekend I saw an ad for Witch City Segway.
Segways instead of brooms? Look at their logo:
You realize that giggling during the rolling of the whirtling invokes a penalty, I assume.
Jetpacks!
When “capes because they are wizards” is a higher consideration than actual game mechanics, I’m going with more.
I know, jet skis or motorcycles aren’t practical; too easy to get squashed between or otherwise have a collision at speed work out badly. Polo ponies could work, except that anybody who’s in a position and of a mind to play such a riding sport is probably just going to play polo.
To my surprise, the game predates Star Trek (although not in the exact form that Kirk and Spock enjoyed): Three-dimensional chess - Wikipedia
Actually, I just looked closer at the site. Capes are not mandatory - they’re certainly not in the rules. One team in pictures has capes, as part of their team uniform. So I would argue that the capes are not higher consideration than the actual game mechanics.
Meh. Every other sport has a uniform. I don’t see anything wrong with the capes.