Ironically, both Yzma and Amzy are on Papa Santos's naughty list.
According to Papa Santos's list, Kuzco has done 2,637 bad things to wind up on the naughty list.
The episode title is a pun on the Christmas play "A Christmas Story".
Giftmas and Papa Santos are obvious puns/references to Christmas and Santa Claus, the later of the two being known in some countries by names that could be translated as Father Christmas or Father Noel.
Kuzco turning into a llama to help Papa Santos is a reference to Rudolph the Red-Nose Reindeer.