Sad that the dog died.
Why is every cop story in the US bate for people to jump on US police officers or the US for violence. Withe the tens of thousand responses every day, "mistakes" happen, criminal acts happen, great things happen, but mostly mundane things happen. The sad part is every single one of those has to be treated the same way, because any situation can turn bad. Spend some time on google and you can see anyone of those things, pulling over Batman helping children, crazy grandma pulling a gun on an officer, officer beating helpless man.
For those that don't know police protocal, and I am no expert, but domestic violence is a violent crime and an officer has to expect violence, he could have a gun, killed her, etc. So going in with his gun drawn is not an issue. He told the guy to raise his hands. A large dog potentially went after him. You have a split second to assess the situation, potential violent criminal who may have beat up someone and potential violent dog guarding him coming after you. Do you lay your gun down, and pet the the puppy hoping to calm him? Not many options in this case. Dogs don't stop when they see a gun like humans, it's a deterant to humans. Pets will still attack. If Dog attacks, all Hell could break lose, sadly for his safety and the safety of the victim (which again, he still thinks there is one), he has to shoot the dog. If he goes down... Lastly, officers respond to calls withouth back up often. Depends on the situation, timing, size of force, etc.
Outcome - do a review of procedures, see if there is anyway to improve the process. As any shots fired, the officer if probably on paid leave. Police Force should compensate the man for pain and suffering, but not extreme. I would sue the actual person who was committing domestic violence. This doesn't happen if there is no call, in which no crime was occuring.