I think the joke here is just that she’s warning her kids to stay away from the weird old man’s house, which is kind of a trope on its own, and then merged with the nursery rhyme. The house she’s warning the kids to stay away from is a squalid, rundown house as you might expect, but it’s funny (presumably, ymmv) to think about what that would look like as a shoe.

I think the Archie references in the Disqus link are just amused by the coincidence that the random name Larson picked is close to the Archie principal, but that probably wasn’t intentional.