To be perfectly honest, I doubt there are dozens of director-level interview samples because there aren't tons of engineering directors, further "director of engineering" is a management, not technical role, so wouldn't be given questions like this, at all, and of the remainder, most of them were promoted from within google, not hired from outside it.
Most new hires get screened in some manner, but very few new hires are directors of engineering, so I'd mighty curious to see your source for the interview questions they got.
What these questions are are the standard set of pre-screening questions asked of a potential SRE IC or maybe TLM candidate. A SWE wouldn't be asked these questions, because they aren't related to the role. A SWE candidate still might get screened, but not with these questions.
A question on Glassdoor (for a Director position) is in the same vein: "How do you tell if a calculator is 8 bit or 16 bit."[1]
[1] https://www.glassdoor.com/Interview/Google-Director-Intervie...
b) That's a different question from this set about UNIX arcana, so it's not the same set
c) All of the other questions on that page are non-technical, so this isn't a question from a standard director set either. (It may be what 'DannyBee said, that people assumed they were being screened for a much higher position than they were actually being screened for.)
As someone who has reverse-engineered calculators, that question has me curious. You could implement the same external behavior regardless of what processor a calculator uses. So I can't see any way to determine the bit width. Is there an answer I'm missing? (Also the question ignores the many 4-bit calculators.)
(Of course you could open up the chip and take a look with a microscope, which I've done. But I don't think that's the answer they are looking for.)
I definitely believe there's a recruiter screening process - I would just be surprised if it's the same screening process they give to new college grads, with the same slate of questions. (Even if you're going to give them technical questions, at least give them harder technical questions!) I obviously have no real information having not interviewed for a director-level position, I'm just stating that these questions seem like the same slate I got as a college grad.
I suspect, again, it's more people thinking they are being interviewed for director, when they aren't (or it was long enough ago that it was before leadership recruiting existed)