I understand the distinction between blue and white collar work so to speak but I would still argue that workers and employees in this context are essentially the same, which is why I claim that my response of "the employees work for the director" should be accepted.
Not true, this is translatorese. It assumes that workers are manual labourers, but white collar workers are still workers, as people doing work. Employees are employed to work. The subtlety is that 'worker' can have a derogatory sense, so we use employee to mean 'robotnik' in many of the situations one would use 'robotnik'. This is the problem with relying on translation dictionaries and education - no one is out there measuring the result of the dictionary choices.
The truth is, it's quite a vague position. It's surely someone in power, but hard to say anything more. I think the CEO is most likely to be "prezes", but that also just depends on the structure of a specific company. You can have a lot of "dyrektor ds. XYZ" (ds. = do spraw) which is like "XYZ director" in English.