He has in fact killed more than one...
...I believe it is actually a total of five. Three of these were at the request of Animal Control (as they are not armed -- due to restrictions imposed on them by the County Commissioners -- even though they are sworn peace officers with arrest powers). Of those three, two were dangerous and vicisous -- 1 had attacked already bitten a citizen -- and the third was suspected to have rabies and after testing was confirmed. The other two dogs he's killed, one was struck by a car and the owner requested he "put it down" and the other was Max, who bit him.
No police in this area, carry 9MM... some are .357 and most are .40 -- with any officer, highly skilled or not, unless they repeatedly train in high risk, high stress training (like SWAT/EST/SOT) the stress and panic of being attacked can seriously impede someone's aim. I've seen training videos from police cruiser dash cams, where police officers and suspects have emptied complete magazines at each other standing only feet apart and hitting nothing. It has very little to do with their shooting ability and a lot to do with panic and stress.
I can see how it is feasible for it to have taken 6-7 shots to take this dog down.
Are you a hunter? What happens when you shoot a deer? Does it get hit and immediately drop right where it was standing? Of course not, but your intent isn't to neutralize a threat, it's to get a trophy and some meat. That shot that hits the deer, the deer runs off and dies hundreds of yards away... you have to track it after one shot. I'm sure if you were to shoot multiple shots and hit it multiple times, you wouldn't have to track very far...
Long didn't want this dog to run around for a few minutes and then die, he wanted it to stop attacking him. He kept shooting until the threat stopped -- if it took 6 shots or 6 magazines -- then that's what he needed to shoot.