Hello,
Thank you for your query at DoctorSpring.com
I understand your concern.
Since you do not have any cuts and your skin mucosal layer was not exposed, there is no chance you can contract Rabies and hence you should not worry.
Moreove the way you described the puppy's characteristics, that he was playful and friendly, it rules out Rabies. Most Rabid dogs will have a very aggressive personality and won't be much interested in food or water. Such dogs are difficult to contain in one place for a long time. There is an other extreme called silent rabies, where the dogs won't be aggressive. However they will be extremely silent and won't socialise.
So either extremes, the dogs won't be playful and friendly like the puppy you played with.
So kindly do not worry. Moreover all puppies keep mouthing because of the pain in the development of teeth in this age group and it is extremely normal.
Let me know if you have any other queries,
Regards.