What should I expect from a non-academic interview for a PhD position? I have applied for a PhD position in Physics. First I had Skype interview that they called "personal interview". They asked me about my family and stuff.

Now the University has called me for a face to face interview and they are calling it "non-academic interview".

I wonder what kind of questions should I expect from this interview?

Note: I had academic interview with my prospective supervisor, who's accepted me.

The university is KAUST (Saudi Arabia)
It is quite acceptable to ask who you will be interviewing with, and what the interview will be about. You can even ask whether you should prepare an overview of your academic work for non-academic interviewers (to which the answer is likely to be "no", but it'll probably be "No, the interview will involve X Y and Z"). You can ask whether it's an interview with their administrative personnel, or with higher-level managers; you can ask whether you should bring anything (you're visiting Saudi Arabia, right?); and so on. You could even straight-out say "I'm not sure I understand what a non-academic interview means, as after I'm interviewing for an academic position and KAUST is a university."

Don't ask a zillion questions, though, just pick one or two depending on the context.

Also, if you know someone who's not in charge of the hiring process (PhD candidates, post-docs, faculty) you can ask them in parallel about the process.

Finally - I could speculate about what "non-academic" actually means: Maybe it's an HR-style interview? Talk with group members to see whether they like you? Negotiations of employment conditions? Political screening like @Ben suggests? ... but they will probably just tell you (except for that last option I guess).