Suppose that somewhere in the galaxy there is a planet where there are large six-legged animals with an inner supportive structure, that evolved completely independently of any forms of life on earth and whose genetic structure is not based on DNA but another molecule. What I said seems perfectly possible. But it is impossible if animals are simply the members of the kingdom Animalia, since the six-legged animals on that planet are neither DNA-based nor genetically connected to the animalia on earth.
On the other hand, the supposition that somewhere (maybe in another universe) there is water that does not have H2O in it is an impossible one. So is the supposition that there are horses without DNA.
So the kind animal is disanalogous to the kinds water and horse. The kind water is properly identified with a chemical kind, H2O, and the kind horse is properly identified with a biological species, Equus ferus. But the kind animal does not seem to be properly identified with any biological kind.
One can have DNA-based animals and non-DNA-based animals. If the Venus fly-trap evolved the ability to move from place to place following its prey, it would be an animal, but still a member of Plantae. Animals are characterized largely functionally, albeit not purely functionally, but also in reference to the function of their embodiment—there cannot be any animals that are unembodied.
Is animal a genuine natural kind? Or is it a non-natural kind, constructed in the light of our species’ subjective interests? I don’t know. I take seriously, though, the possibility that there is an "Aristotelian" philosophical categorization that goes across biological categories.