That post was by the original farmer asking for advice, why would he have thought about that if it hadn't thought he could do it with pop gun of a rifle.
.22 rimfire is a common calibre for captive bolt guns. We have different loads for different size pigs. Presumably there's a cartridge out there for cattle as well.
The wire-jiggling bit is called pithing. It's one of the two ways to legally kill an animal with a bolt gun (the other being bleeding).
Legally speaking, bolt guns are only considered a means of stunning an animal, although in practice they are very effective at killing an animal outright.