First time I've ever posted here, and such a miserable topic. That poor beagle it looked like those two dogs were doing to it what my cat does to mice when he catches them.
My take on the behaviour: the dog coming toward the officer was bouncing to a halt, you know how some dogs do, they're happy to bounce right up barking etc BUT when what they're barking at doesn't move they kind of bounce forward the last few paces then bounce a final time on the spot before continuing to bark because they're unsure.
Anyway, IMO the officer was in the right, those two dogs had NO right to be in that yard regardless of how the beagle is housed or what the owners of the beagle did or didn't do and irrespective of whether there was another way there wasn't that much time on the video between the officer entering the yard and the shots being fired. We can all sit and say I'd do this or I'd do that all we like, facts are it didn't happen here, and you don't know how you'll react until you're in that situation which I hope never happens to any of you. I'd certainly want the dogs removed from my yard as quickly as possible and as humanely as possible. It wasn't an ideal shot, but seriously, he was lucky to hit it at all IMO, he hadn't even aimed properly for the first shot because there wasn't time...
Just my two cents :)