The simplest part of it is that it's about parallel universes; the "garden of forking paths" that doesn't actually appear in the story is time splitting, and sequences of events happening, and happening different ways in different universes. The book in the story is trying to express that without actually coming out and saying that it's about time, hence the bit about how a riddle whose answer is chess cannot use the word "chess." ...that's all I got. I'm used to the idea of parallel universes, so I got that right away, but I'm not entirely sure how to connect the idea of parallel universes with the idea of riddles.