Article mixes "elites" and real elites. The mere usage of the term employment is a dead giveaway, among other issues. Real elites are not employed by someone as a general rule, with some exceptions of course. Article would be more aptly named "Overproduction of qualified or overqualified workers".
It's been awhile since I've read Turchin but I'm pretty sure in his own examples elites are indeed employed in prestigious positions. Which is really his whole point, there are only so many prestigious positions. His example using musical chairs has always stuck with me.