When discussing the same technique used for therapeutic cloning the Reuters story quoted him as saying that
...he is not cloning human embryos, but using eggs harvested from human females, infusing them with genetic material, to create cells that can never become human beings.
"I firmly reject the term human cloning," Hwang said in an interview with Reuters in May. "This is a scientific activity called somatic nuclear transfer, and in no part does it involve the physiological process of fertilisation of eggs by sperm."
So, there you have it -- no sperm, no human -- and by extension, no dog. Snuppy was made using eggs harvested from a female dog, infused with genetic material and thus he can never become a dog.