A really rough breakdown is an employee is somebody who is bound to the directives of the company he is working for. Ie. cant by themselves choose their working hours freely (amount as well as time) or what they are working on.
This looks somewhat ok for a more in-depth explanation:
https://www.howtogermany.com/pages/employee-employer-relatio...
Your link notes that managerial positions carry certain exemptions, which is true in my country too, but that doesn't preclude managers from being employees.
Directors are generally not considered employees unless they also work as an employee serving some other function in the business. This appears to be true in Germany as well. Are we simply mixing up directors and CEOs?
They ruled only that in the specific case that the CEO was also an employee (when being fired), but they did not rule that CEOs are always employees under all circumstances.
The source below has some good extra points why its such a complicated issue.
Source (in German): https://www.steinberg-arbeitsrecht.de/de/blog/384-wann-sind-...