What Boyd is arguing against, and suggesting that the new generation should be arguing against, are certain ideas that he associates with French poststructuralism.
A “greatest generation” of iconoclasts established two fundamental principles: first, anti-foundationalism, the idea that there is no secure basis for knowledge; and, second, difference, the idea that any universal claims or attempts to discuss universal features of human nature are instead merely the product of local standards, often serving the vested interests of the status quo, and should be critiqued, dismantled, overturned.
What philosophy students might notice is that lit studies might have adopted these ideas in 1966, but Nietzsche argued for them in the late 1800s. Let's be honest though- Nietzsche wasn't arguing that those 'myths' should be overturned, but countered with myths. I would also suggest that Nietzsche eventually denied anything outside of 'myths' and 'art'. Also, I might be wrong (as happens), but I think that 'anti-foundationalism' has a foot in Kant too.
Anyway, these ideas have, apparently, become commonplace in literary studies. I would argue that they have become common in historiography that aims at 'discourse analysis'- actually, most cultural history really, and have been as unquestioned there. There's a lot of timidity amongst newer scholars... an unwillingness to challenge the status quo of the profession. So we see a lot of newly minted PhDs whose dissertations are on a "Foucaultian analysis of 1920s janitors" or whatever, basically rehashing the same old arguments. In a way, it reminds me of psychoanalysis, in which there has never been a successor who could equal Freud, but more diminishing returns from his epigoni.