The purpose of the pet snack is to get the multipet skill. However it appears that Royals intends to allow us to use multipet even without completing this quest. Multi-pet is just currently disabled due to a bug that will make people dc. But anyways, I believe in GMS, the pre-req for the pet snack quest is to finish the Henesys Pet Park JQ and get the letter from the basket at the top. It seems this pre-req quest is bugged at the moment, which is why we aren't able to do the pet snack quest.