Where does the primary interest of the story lie? What are the principal sources of appeal? Does it illuminate human character?

Generally the "primary interest" of a story is centered on the plot, character(s), theme(s), and so on.  For the story "A Christmas Memory," I believe that a case could be made for each of those things being the primary interest of the story, so feel free to defend each choice as you see fit.  For me, I would choose the story's themes as the primary interest.  The story contains various themes, but I believe that the theme of friendship stands out more than the other themes.  The story is focused on a relatively short amount of time that Buddy and his friend spend together, but it is clear to readers that the two friends deeply love and appreciate each other and the time they get to spend with each other at Christmas time. 

It's always the same: a morning arrives in November, and my friend, as though officially inaugurating the Christmas time of year that exhilarates her imagination and fuels the blaze of her heart, announces: "It's fruitcake weather! Fetch our buggy. Help me find my hat."

Their friendship is quirky and goofy, and it shows the reader that two people can have fun doing just about anything as long as they are together.  Their friendship is "tested" by other adults that tell Buddy that his friend is a bad friend and a bad influence, but Buddy wholeheartedly disagrees.  

Listen to what they have to say, the words tumbling together into a wrathful tune: "A child of seven! whiskey on his breath! are you out of your mind?"

Another supporting example for the theme of friendship is that Buddy and his friend are making their 31 fruitcakes for "friends."  

Who are they for?
Friends. Not necessarily neighbor friends: indeed, the larger share is intended for persons we've met maybe once, perhaps not at all.

They go through a lot of time and work to get those cakes made and delivered, and this shows readers that there is value in doing something nice for friends and neighbors.  
By main "sources of appeal" I believe that the question is asking about the ethos, logos, and pathos.  Ethos deals with credibility, pathos deals with emotions, and logos deals with logic.  For "A Christmas Memory," I believe the main thing that appeals to readers is the pathos that is contained within this story.  Most readers are going to enter this story with their own memories of Christmas time and specific family traditions.  Most readers will also generally have very fond memories of this time of year because of the food, family, and laughter.  This story has all of that.  A reader cannot help but feel good about Buddy's adventures with his friend.  They are giddy with excitement for everyday tasks like going to the store, picking out a tree, and flying some kites.  They even literally get giddy with a bit too much whiskey.

My dancing shadow rollicks on the walls; our voices rock the chinaware; we giggle: as if unseen hands were tickling us.

I do believe that this story illustrates and illuminates human character.  I think that is why the story is such a fun read every time.  My students may groan at having to read an assignment in class, but that does not stop them from giggling with each other while reading through this story.  That happens because this story resonates with each of them on a very real and personal level in one way or another.  Stories that do not illuminate human truths are stories that readers do not typically enjoy reading.  They do not see the point. However, this story absolutely sparks lively discussions about personal Christmas traditions and things that happened at family gatherings.  Readers are very willing to open up about how they love a particular family member's friendship even though they only see that person once a year.  This story clearly illustrates that friendship is an important human value.