The author is using "dying-earth genre" to mean something rather specific that the series Dying Earth, despite the name, doesn't necessarily fit. I haven't read it, but going by Wikipedia it sounds like it has at least as much in common with the "sword and sorcery" stuff she mentions later as it does with the absolutely bleak stories she excerpts by Wells et al. I've read a couple of Wolfe's books (Short Sun, IIRC?) and I would definitely put them in her later category, even if "sword and sorcery" undersells them enormously.
Reading further on Wikipedia though, she might have picked a bad/already taken name for her category. https://en.wikipedia.org/wiki/Dying_Earth_(genre)