Moving this thread to a more appropriate boardWhile what DF has posted is interesting, it has very little to do with the calendar entry.
Just what is a mooncake for a Pagan and why does it have a day?
Depends on who the Pagan is ... The Day of Mooncakes is a
Celtic celebration centered around the Moon Goddess.
Are mooncakes part of Cakes & Ale?
No
Or does it have something to do with the New Moon?
Nope
Because the ancient Celtic religions were mainly oral traditions, there isn't a lot of information available from an anthropological standpoint so there won't be much that can be found online about any of the lesser holidays, celebrations, or traditions they held. Don't know why the day is named such, but a mooncake was likely a bread based food created to honor the Celtic Moon Goddess.
This celebration was included because at least one of the staff here observes Celtic celebrations. We'll be happy to include observances of other traditions or pantheons but those items need to be requested as the admins do not have time to research every single Pagan observance.

As an aside ... do not try to learn about anything solely from the internet ... much of the information found online is flat wrong (including some information found on many public forums). Online research if fine if you can sort the wheat from the chaff, but any research needs to be heavily augmented by reading knowledgeable resources (such as books written by recognized experts).