if someone follows the definition of the process as laid out in the literature,Agile has no "process as laid out in the literature".
I'm not even sure where this idea comes from.
The Agile manifesto is extremely basic. It contains a few core principles, and everything else is elaboration on them.
This organization is violating even those very basic tenants.
It's possible that, over and above the manifesto they're trying to implement Scrum or Kanban or some other process, and heck, they may be failing to adhere to those processes as well
But if they're not at a bare minimum attempting to live and breathe the values encapsulated in the manifesto, they are by definition not executing an Agile process, since the manifesto defines what "Agile" is.