Self-defense from a legal standpoint is whether the person in his mind felt threatened and a reasonable person in the same situation could react the same way.

In this case, as Skeeter said, once the guy got his dog away from the alleged attacking dogs and into the house, the threat had ended. So unless there was further fear of damage to livestock or property, he no longer had a legal right to go out and shoot the dogs. Once he had his dog in the house, he should have dialed 911 and reported the "stray" coonhounds running around his property.