Predators rarely do this, the don't play with their meals as you could see the Cheetah licking the fawn. But this phenomenon has been documented on few occasions when a predator shows empathy of a baby prey captured alive, its beyond comprehension how cold blooded killers could have soft spots and could exercise some sort of kindness like they do to their own offsprings.
The big cats family are peculiar to this strange act, just like the Cheetah, pride of lions, solitary Leopards and Tigers have been filmed petting baby animals, some of which they have killed the parents some they hunt down but grow cold feet to kill. A popular video circulated the web about a Leopard that killed a Monkey, found out the money had a baby and catered for the baby monkey for three days before it died.
Wild animals have some level of intelligence as humans, this is a demonstration of it. By their natural instincts, they hunt to kill and eat not turn surrogate mom or dad or perphaps distant uncles. But we can't explain this rare occurrence, just like thousands of nature's mysteries yet to be unfold.