People who are good at math, but not mathematicians, will get it. There is very little hope of explaining P and NP to people who feel nervous in the presence of math and don't want to hear what a "polynomial" is.
Speaking of math, do you think you could throw a few integrals into some post, or a sequel to "Technical Explanation of Technical Explanations"? I have a friend who's mildly interested in LW because I read it, but isn't willing to read enough to solidify an opinion without that s-shaped signal of competence.
If you read the entire section from the beginning, you'll notice that you don't really need to know what a Hamiltonian cycle is to understand the explanation. A made-up property would have worked equally well.