I am not an expert on legal realism, nor do I intend to become one. But I have been reading quite a bit on the topic because I think it is highly relevant to understanding modern legal scholarship and the "industry" of legal education--i.e., it's crucial background.
Brian offers the most succinct rationale I have read for the pervasive influence of legal realism and why we shouldn't lament the failure of the original realism to develop an empirical component in the tradition of the social sciences:
The actual Legal Realists ... paid homage to the social sciences, even adopting the rhetoric of the then-dominant behaviorism (e.g., talk about the "stimulus" of the facts of the case), but their actual scholarly practice was almost entirely insulated from the social science of the day ... .
This isn't to say that the Realists weren't interested in what the courts do in fact, it's just that their approach to the facts about what courts do almost entirely eschewed social scientific inquiry, and for good reasons I think. The paradigmatic Realist inquiries of the 1920s and 1930s [citing lots of examples] ... consisted in careful scrutiny of the underlying facts of lines of cases, bringing out the gap between the official "doctrinal" explanation for the decision and the actual sotto voce norms that seemed to be at work in the judge's thinking. The goal was to discover the non-legal norms that made best sense of the courts' response to recurring "situation-types," i.e., patterns of fact that seemed to elicit the same kind of results. ...
That the preceding was the heart of the Realists' "empirical" method explains, of course, why the Realists were so influential in American law: you didn't need social science training to do this kind of analysis, you just needed to be a sensitive and skeptical reader of court opinions, something good lawyers are, well, good at. ...
A "new legal realism" would continue the paradigm of scholarship established by the old legal realists, namely, contrasting what courts say they’re doing with what they actually do. "We are all realists now" because this is what so many legal scholars do, including those who know nothing of social science and don't even self-identify as realists.
These are interesting and important points. From my own perspective, NLR is really about developing a theoretical framework (or a workable consensus) on how and when to utilize relatively new research tools and perspectives; and this requires a renewed engagement with the social sciences, which have changed a lot in theory and method since the 1930s. As Stewart noted in a comment, we should not overinterpret the name "new legal realism". Picking the name merely started a worthwhile conversation. If the conversation continues over a period of years, the NLR label will grow legs.