It has always been held that destroying pests or varmints (or predators where necessary) is perfectly valid.
Gophers and prarie dogs are exceptionally destructive. Shooting them is just a valid way to control population.
Personally i don't care for the video. I think it makes the deaths of the animals gratuitous and glorifies the killing, which i don't personally think much of. But that's me. Killing gophers is a 'must do' on the praries.
Generally i don't go out of my way to shoot varmints and the like without a reason, but it is something that's part of management of the wild.