Typically, "natural" means "not of human manufacture". That it's general meaning, and how it is meant in this case too.

That's not quite true. Natural selection is typically contrasted with artificial selection, in which individual traits are deliberately selected.

In the case of poaching, poachers are not intentionally trying to change the phenotype of the animal. They want to collect the horns/head/etc. The selection itself is an emergent side effect and, I would say, the natural result of a highly effective predator being introduced into the environment.