I was thinking he probably could have gotten a trespassing complaint on them, but once he shot the leashed dog, it all falls on his head. That is just wrong. I agree he could have shot the dogs before they got there, but even then, it sounds like they weren't threatening him.
That said, an uncle used to be a ranch manager for a rich guy on 800 acres near where I grew up. It was mostly light woods with some pasture. He said if they have seen packs of dogs (as many as 15 or 20) running through that land at night, some wearing tags, some not. He said they shot as many of them as they could before they ran off. They would generally take off at the sight of people. Hunting dogs like this especially when the owners are right there is a whole different story.