They can't shoot the animals, because that renders parts of the animals useless. They can't use that for food. That's why shocking them would be the best method imo, because at least that would end things quickly.
Snapping the neck can usually kill animals instantly, but as shown in the OP's video, the workers don't really have any training it quickly killing animals. And that's important training that is lacking. If you don't know how to snap a neck, you're going to end up putting the poor thing through excruciating pain.