Having never heard of wild beagles before I'm curious what sort of test they perform to determine it. They are a fairly small dog, yotes around here would have it for dinner rather quickly.
There are legalities, and lying, possibly being inhumane with a kill (which would seem not to be the case here), and possibly killing someone's pet...
...but there's no inherent immorality in killing a dog any more than a coyote, rabbit or deer.
I guess I don't see where this was animal torture in any real capacity. That's like saying hunters torture everything they kill. It was a shot in the heart, which any hunter would be happy to have made.
I understand the anger in him shooting a random dog for no apparent reason. It just doesn't seem like "torture" is the best word to describe it.