His books can be like They Might Be Giants songs for me, often having abstruse deeper meanings if you wish to dig, or you can just skim the top and enjoy the frivolity and madness dancing on the surface.
Or you can do both!

I think you are pretty much right about the meaning of the quote. It's about delusion and apparent truths, I think- seeing what you want to believe, etc. The cat's cradle is a silly child's game that he finds analogous to "silly games" adults play that have more serious consequences.