There is no doubt that kinetic energy transfer is what kills. But the idea that one can specify a minimum requirement for any particular species is what is a crock. The different projectiles in question have different requirements for making a kill. Arrows, for example vs shotgun slugs vs rifle bullets vs pistol bullets. You can't specify a set figure of foot-pounds for any one of these that would be applicable to the others. Or applicable to the next round you fire, either.

(The requirement for 1000 ft/lb AT 100 yards and an 85-grain bullet for elk and moose is pretty liberal! I think the 223 Rem can be loaded to meet this requirement .)