I can see why the guy's is pissed about his dog. I have a dog myself, and I would be pissed if someone injured my dog.
However, the guy on video is overreacting. It could be genuinely or it could be him looking for blue money.
Nevertheless, we don't know the details of the case, or what exigent circumstance the officer had for him to shoot the dog. I doubt the officer woke up and said "I feel like shooting a dog today..."; not to mention that firing the service weapon while on duty holds tremendous liability and accountability. It sucks that a dog had to die, but if the officer felt threatened (assuming he had legal justification to be in the property), he is justified in putting that dog down.
OVERreacting?! The guy stayed cool and reasoned as hell considering his circumstances.