Yes, the puppy is a finger chewing monster.
I'm not putting blame on anyone here, but I would hardly call this dog a monster. Almost every puppy or kitten I have ever met likes to nibble on fingers, Corkscrew still tries to bite my toes at night, but that doesn't make him a monster. The reason why Corkscrew stops biting me is because I pull my fingers or toes away and say "No" so he knows he has to stop. But I know if I just sat there and let him and my toes weren't moving he would continue to chew unless there was something to stop him, but I wouldn't say he was unwell or a monster. I'm assuming that if the mother was letting the puppy sleep with the child he hadn't shown signs of aggression. How is a young puppy supposed to know that what he was doing was wrong? The fingers smelled like dinner and they weren't moving and nothing was being done to tell him he was doing wrong. To him the fingers were no different then a dog bone or anything else that smells like food.