If the cat was clearly threatening an endangered species, I think that this man was within his rights to stop the cat from preying upon said species.
But firearms did not have to be used at all. Relocation of the cat, adoption maybe, or give its "owner" a stern warning about allowing his pet to kill an endangered species.
If he did really think that the only possible way to protect the birds was to kill the cat, then indeed shoot shovel and shut up would have been his best route. He also should not have let the cat suffer, he should have used a second shot to stop it from experiencing a slow death.
Indeed, it is sad that the cat died, doing something only natural. But for some humans, defense of an endangered species is also natural.