Scott Fleischman: they do say, at the top of p. 11, "Contrary to the definition we've chosen, the term poset frequently is used to mean partially ordered set, rather than preordered set", but their wording makes it sound like it's more of a convention that they took one choice on, rather than a complete break with standard definitions. I too am curious why they went this route. If preordered sets are somehow easier to work with, they could use them but still call them the right thing.