"Moral Relativism, RIP"...and What I'd Like to See in Such Articles

This is ok.

There are a few points in it that should be made more frequently. E.g.:

There are traces of relativism in pluralism, freedom of speech, cosmopolitanism, foreign-policy realism, and a thousand other principles, including many that conservatives like. With the help of good judgment, these concepts have allowed the West to find a middle ground between nihilism and absolutism. Promiscuous use of the R word only makes that project more difficult. 

As for the first point, sorta, but not exactly. There aren't "traces" of relativism in e.g. pluralism and freedom of speech, really, though relativism does intersect with liberal democratic views on certain specific issues--kinda. One type of relativist--though not all types--would think that other individuals have no right to tell me how to act in my private life; we, the heirs of Jefferson, would agree, but not because we are relativists. We don't think that all decisions one might make about ones private life are correct by definition--we don't think that rightness supervenes on belief. Rather, we think that some things people do in their private lives are damn stupid, and some are morally wrong...and yet we have no right to use the coercive power of the state to stop them from doing those things, so long as there's minimal collateral damage to the rest of us.

Foreign policy realism intersects with certain forms of social/cultural relativism in certain ways, but, again, the resemblance is rather superficial. FPR in its pure form holds that we are objectively obligated to do what's in our narrow national interest. That makes for a state that is, with respect to its interactions with other states, egoistic (roughly: sociopathic). FPR thinks states should be unconstrained by morality with respect to interactions with other states. The relevant versions of relativism think that moral obligations are defined in terms of collective inclinations. In brief, FPR is an amoral view. The relevant versions of relativism are far weirder than that; they define rightness in terms of traditions and inclinations. Such views peg the needle on the weirdness scale; by comparison, FPR is hardly even odd. Thinking that you shouldn't be constrained by morality is bad; thinking that you are obligated to act in accordance with the traditions and inclinations of your society or nation...that your inclinations, beliefs and traditions create genuine moral obligations...well damn, man...that is weird on weird.

Here's something the author is right about: the promiscuous use of the term 'relativism' does, indeed, make such discussions very difficult.

Basically, it gets used to mean "any non-standard view." And that's all wrong.

Cultural moral relativism, for example, has got to be something like the view that tradition defines/grounds/subvenes/whatever moral obligation. If it's not something like that, it fails to be anything at all. Any other theory of the view makes it collapse into nihilism, or fallibilism, or skepticism, or utilitarianism, or egoism, or some other already-occupied sector of conceptual space.

Consider:

Relativism has become such a routine charge that half the people who invoke it feel no need to do more than gesture toward the culture at large by way of explanation.But we’ve come a long way since the days when Marilyn Manson and Andres Serrano (the artist behind Piss Christ) could make careers out of transgression for transgression’s sake. Breaking taboos for shock value is relativism; breaking taboos as a means rather than an end is not, which gives Lady Gaga and Seth MacFarlane an alibi.

No, relativism is not transgression of cultural norms, and "breaking taboos for shock value" is not relativism, and has nothing to do with it. Breaking taboos for shock value is...well...I dunno whether it even has a name. Does it? The cultural moral relativist holds that breaking taboos is morally wrong--really morally wrong. It is deserving of punishment. It's bad. What makes a cultural moral relativist a relativist is that (i) he holds that there are no objective, universal moral obligations, and (ii) he holds that traditions, taboos, practices and social norms generate/subvene relative obligations. Such relativists are distinguised from nihilists in that they think that there are real moral obligations, obligations which are every bit as obliging as realists, rationalists and universalists think they are. They are distinguished from realists, rationalists, and universalists by thinking that morality can be grounded in something that seems patently irrational, arbitrary, and incapable of surviving rational reflection--something non-transparent to use Christine Korsgaard's term.

Anyway, even my discussion here is too hasty. But, if taken seriously, it would do more good than harm with respect to understanding relativism. I have, however, asserted a few non-standard views here, and only barely defended them.