There is no question that energy is required. Without energy transfer, nothing happens.
Yes but we're talking about bullets killing animals, not the laws of physics writ large. There is no question about whether any bullet not at rest has "energy."
Even with massive energy transfer, if it happens over a large enough area or time span, nothing interesting happens.
Those two facts should lead one to the more interesting questions and useful answers.
Once again, bullets and animals. Bullets impart their energy in a small area over milliseconds.
The question is, in that context is "kinetic energy" a good yardstick.
And the answer is no.
