That opening paragraph – with the dreams and the older-still dreams, and “Go west” and how the Corinthian's part of that dream now. Oh that's good. Makes him seem more a force than a being in many ways. (Also a kind of 'Slouching Toward Bethlehem' feel to it that I like.)
Observations of “American dreams,” and the idea of nightmares coming out of the country's ash – the social commentary works too.
Blood and body fluids as the only moisture in the landscape. Pervasive, but there's a subtlety with the writing that keeps it from becoming repetitive-boring. That image of how the fluid would look like mud, except there is no mud, drove it home for me. Then there is Vino and the wine bottle, and I like that he's “Vino” here more than anyone/anything else, as the first bit of wet since the last body.
And oh man their meeting. Curiosity instead of fear, and, since you've established the Corinthian so well, it makes Vino/RT start to seem more legend and less human himself. Gives a sense that Vino/RT is/could be part of that mass dream.
I like you mentioning the Corinthian's 3 mouths, and all 96 of his teeth aching. It makes him seem more not-human. (It's also one of those “yes, Gaiman would do that” touches.)
...TL;DR version: It's awfully good, it reads a LOT like Gaiman-verse, and the Corinthian's narrative voice seems spot on to me.