That's just a weird story. They're probably both nuts. Who would be insane enough to handle an annoying neighbor's chihuahua with a pellet gun? D'oh! I'd suggest a paintball gun.
However, the idea that the dog was barking aggressively? Was this after the shot or before? Wouldn't you think the dog would be yelping, at the very least?
It is my understanding (not from the article but from neighborhood gossip) that the guy was trying to do some work in his yard and the dog was constantly yapping away at him through the fence. I guess then the guy got frustrated and went and got the pellet gun.