One is the non-reductionist metaphysical doctrine that the normative is sui generis and unanalysable into non-normative components or in purely non-normative terms, leading some writers to classify views as forms of ‘non-naturalism’ on this basis.
means Moore thinks you can't reduce 'ought' claims to 'is' claims, roughly.
The other legacy is the epistemological doctrine of intuitionism: that some substantive or synthetic normative truths are knowable a priori.
means that Moore thinks that you have access to informative moral truths (like 'it is wrong to kill wontonly' and not just 'murder is illegal homocide') in such a way that doesn't make reference to any particular experiences or contingent facts about the world. So Moore thinks that you can know 'it is wrong to kill wontonly'' independently of knowing any of the specific facts about human beings or human societies or anything like that.
But right, non-naturalism is a possibility for normative theories (and not a particularly unusual one, since all Kantians would count as non-naturalists). I'm not a non-naturalist myself, but I suspect cousin isn't getting away with eliminating the 'ought' in referring to utility functions, but just hiding it in the utility function. But I'm not well versed in that sort of thing, so I don't think I'm quite entitled to the criticism.
I find Eliezer's explanation of what "should" means to be unsatisfactory, and here's an attempt to do better. Consider the following usages of the word:
All of these seem to be sensible sentences, depending on the speaker and intended audience. #1, for example, seems a reasonable translation of what a pebblesorter would say after discovering that X = Y*Z. Some might argue for "pebblesorter::should" instead of plain "should", but it's hard to deny that we need "should" in some form to fill the blank there for a translation, and I think few people besides Eliezer would object to plain "should".
Normativity, or the idea that there's something in common about how "should" and similar words are used in different contexts, is an active area in academic philosophy. I won't try to survey the current theories, but my current thinking is that "should" usually means "better according to some shared, motivating standard or procedure of evaluation", but occasionally it can also be used to instill such a standard or procedure of evaluation in someone (such as a child) who is open to being instilled by the speaker/writer.
It seems to me that different people (including different humans) can have different motivating standards and procedures of evaluation, and apparent disagreements about "should' sentences can arise from having different standards/procedures or from disagreement about whether something is better according to a shared standard/procedure. In most areas my personal procedure of evaluation is something that might be called "doing philosophy" but many people apparently do not share this. For example a religious extremist may have been taught by their parents, teachers, or peers to follow some rigid moral code given in their holy books, and not be open to any philosophical arguments that I can offer.
Of course this isn't a fully satisfactory theory of normativity since I don't know what "philosophy" really is (and I'm not even sure it really is a thing). But it does help explain how "should" in morality might relate to "should" in other areas such as decision theory, does not require assuming that all humans ultimately share the same morality, and avoids the need for linguistic contortions such as "pebblesorter::should".