Look: The cat was behaving oddly, and the idea--as near as I can tell from the article--was to kill it ASAP. We don't know if anything was readily available besides normal-carry handguns. Folks in a hurry don't always stop to think things through. To speculate, maybe all that was available to any officer was a shotgun and he didn't stop to go back to retrieve it from the car.
Worrying about "What gun (cartridge)" is beating a dead horse. Forum members here are supposed to be at least partly clued-in.
Shame it went to the garbage pit, and that nobody popped for the taxidermist fee. Cougar hides make nice rugs. Mine's draped over the back of the couch.