The Egypt Game is told as a cozy yarn, meaning that it sounds like the kind of storytelling you'd hear around a fire on a chilly winter's night. The narrator does a good job of setting the reader up for exciting parts:
Then, just at the beginning of September, with school only a few days away, came that exciting day when the Egypt Game began. (4.18)
The way that the story is told, with emphasis on "exciting" days and grand events, gives it an almost fairy-tale quality.