Humans have a certain affinity for the young of any species. We have selected through breeding for dogs who maintain a certain juvenile appearance and behavior. Adult wolves do not lick each other in this way. Domestic dogs do because it is something puppies do. Puppies (including wolf puppies) do it to stimulate an adult to regurgitate food for them. Wee pups are not able to chew meat, so adult dogs/wolves chew and partially digest the food for them, regurgitating it for them when needed. Baby birds do something similar when they hold their mouths straight up and wide open. It stimulates the adult birds to feed them. Human babies cry to be fed.
Obviously there is no need for an adult dog to ask for regurgitated food, but we have inadvertently bred this behavior into them while trying to capture other puppyish behaviors.