This is correct I think, but confusing. All realists are by definition cognitivists. Non-cognitivist is simply one variety of anti-realist: someone who thinks moral statements aren't the kinds of things that can have truth conditions at all. For example, someone who thinks they merely reflect the speakers emotional feelings about the matter (like loudly booing).
Of the anti-realists there are two kinds of cognitivists: Moral error theorists who think that moral statements are about mind-independent facts but that there are no such facts And moral subjectivists who think that moral statements are about mind-dependent facts. If what you say is true, Eliezer is one of those (more or less).
Yes, people who say that realists are cognitivists say that this is true by definition, but I don't think these terms are used consistently enough that it is a good idea to argue by definition. In particular, I think Eliezer is right to equivocate on whether he is a realist. He certainly rejects the description of his morality as "mind-dependent."
There seems to be a widespread impression that the metaethics sequence was not very successful as an explanation of Eliezer Yudkowsky's views. It even says so on the wiki. And frankly, I'm puzzled by this... hence the "apparently" in this post's title. When I read the metaethics sequence, it seemed to make perfect sense to me. I can think of a couple things that may have made me different from the average OB/LW reader in this regard: