The cop is likely following the training he was given, which is to shoot attacking animals--it's a lot cheaper to replace a dog than to hospitalize a cop, and ultimately the officer's life is worth more than the dog.
I love dogs, I've lived with several (medium and large), but you don't mess around with something like that if it decides to get dangerous.
This is the same reason that cops are trained to shoot center-mass and until the attacker is down; this officer responded quickly under stress and safely dispatched his attacker, preventing possible serious injury to both himself and his partner.
If you want to argue that the cops shouldn't have cuffed the guy, I'd absolutely agree. A polite "Now, son, why were you phoning at us?" would've avoided all this nonsense. I can't in clear conscience disagree with the self-defense the officer used.