Funny political comment aside - As a European I only knew about the New York style before. Although usually with roasted onions.
Which is a shame, because especially the Chicago one looks awesome! What is the filling in the Miami variant?
Seattle style is also a thing if you're into regional dogs.
The meme itself is making fun of the very fake, very racist rumor being spread by the US right wing that Haitian immigrants in Springfield, CO are stealing and eating pets. I don't think it is successful in the parody here, though. If this was coming from an unknown source I would think it is trying to spread that rumor. The only reason I got that it was meant to be parody was the face that Chris is sharing it.