I think I'd agree that it's not really a Christian story, even though it's about Christmas. Whereas, for example, The Lion, The Witch and the Wardrobe is very clearly a Christian story.
But then, Christmas isn't really Christian either!
I did enjoy reading the book, having just seen the 1951 film adaptation with Alastair Sim.
It did seem to me that a glossary is needed for some of the archaic terms and references, but there was nothing that I didn't understand that spoiled the story.
It's definitely written in a humorous style. A very good choice indeed for the book club this December.