If you're confused like me, a "punt" is a long, square, flat-bottomed boat used for navigating swamps and rivers, where the boat driver stands and pushes the bottom of the river with a long pole.
Never heard punt used for anything else but kicking my entire life. Also with how randomly crazy everything is there, it seemed like a perfectly logical action based on their world.
It's the pitfall of nearly every setting where "because magic" is a valid explanation for really anything.
When magic is shown to enable, say, telekinesis, the immediate logical conclusion is that the same method should apply to mundane transport of goods and people. Then when you see the same people using horses, cars, etc. it absolutely necessitates an exploration of the limits of the magic and why it works in one situation but not the other.
I always associated small flaf bottomed boats as being "shallows rafts" or "swamp boats" depending on context. Im from Southern California though, we dont have water.
Even if you'd never heard of the boat type, it seems easy enough to just assume from context that "punting" was some weird British-ism synonymous with ferrying, rather than Filch drop-kicking students.
Frankly speaking Filch drop-kicking students is entirely in character. Also us Americans will 100% accept weird shit if it doesnt try explaining itself. We have to exist within the same environment as opossum and racoon after all.
In character, sure, but physically improbable. Maybe Hagrid would've been big and strong enough to drop-kick teenagers dozens of feet across a swamp, but not Filch.
I always viewed it as filch being so threatening and such as his guise. If he actually kicked a student everyone would know he was a squib so much quicker/surer and he'd get picked on so much more.
The twins are "respectful" in their picking on filch usually, but others might not be so.
Ironically as a Canadian who had never run into this usage of punting I actually put it together thanks to my random knowledge of the Punt Gun, a massive single-shot shotgun from the Victorian era used to hunt entire flocks of waterfowl with one trigger pull. They were so large and powerful they couldn't be safely used when held by a person, so you'd lie down in a boat and brace it against the boat (which I suppose is now termed the punt)
They were eventually shunned due to being considered unsporting (and decimating the local population of bird with ease.)
I learned the term from a dirty limerick in a sci-fi anthology about dinosaurs that I picked up in middle school at a school library book sale. It was told by a telepathic tree which was trying to convince a guy to jack off into a condom and shove an acorn in it so it could reproduce, as that's how it had been created. It was weird.
I was equally confused as a kid talking about how Harry and friends would have a row in the common room, and me trying to figure out why the hell do Wizards have boats inside.