But I wonder, can I (not a student anymore) be denied for that position simply because I am not currently at university?
Yes. Werkstudent is similar to an internship or co-op. It's a specific arrangement for students so they can get some exposure to the real world and do something useful in the process. The intent is quite a different from regular employment. Typically the idea is:
- It's time limited. There is no expectation of permanent employment. When your time is done you go back to school.
- Onboarding is limited: since you are only staying for, say, 3 months or so, the company is not going to invest in a full onboarding process.
- Compensation is small-ish and sometimes zero.
- Benefits work differently. That depends a lot local rules but for example, you may be expected to have health insurance through your student status.
- It's often a requirement for some decree courses and the university will manage the paperwork around it.
In most cases, it really doesn't make sense to hire a non-student for this type of position since it's specifically designed for students.
It's not unheard of to have fresh graduates do an internship if they can't find something else, but it's not the intent and not a great situation for either party.