…but this author doesn't realize that. He writes:

Influenced by Karl Marx, Frankfurt School philosophers such as Adorno and Horkheimer were alarmed at how industrial capitalism had undermined the Enlightenment….

Disciples of Marx, Adorno and Horkheimer diagnosed the failure of Enlightenment, evidenced by the dark events of the twentieth century, as stemming from a division of reason into objective and instrumental reason. Objective reason involves an autonomous assessment of the intrinsic value of the ends we pursue. Instrumental reason involves figuring out the most effective means to achieve those ends. Adorno and Horkheimer argue that instrumental reason eclipsed objective reason in the age of industrial capitalism. People no longer asked themselves whether the ends they were pursuing were intrinsically valuable.

This is not a bad gloss on Adorno and Horkheimer, but it has almost nothing to do with Marx:  A&H were certainly influenced by Marx, but they weren't disciples, in part because, unlike Marx, they had not overcome Hegel.  The idea that the "dark events of the twentieth century" arose from "a division of reason into objective and instrumental reason" is the kind of nonsense only a Hegelian could believe, but certainly not Marx after he cured himself of Hegelian idealism in favor of a naturalistic method (eschewing Hegelian internal critique in favor of something like inference to the best explanation) for doing philosophy.   Althusser had a crude and obscure version of something like these ideas about Marx, but Anglophone philosophers have, quite reasonably, ignored that; what will be the decisive reading along these lines is now due to Lawrence Dallman, a recent PhD from here, which will reframe the philosophical reception of Marx. (Of course, one cannot fault a writer for the online Areo Magazine for having a simple-minded understanding of these issues.)