I've been at Google for five years as a SWE and I've been interviewing for 3 of those. I'd fail this pop quiz. This strikes me as bizarre and inconsistent with all the practices I'm aware of. The idea that we'd ask anyone this stuff, let alone director candidates, strains belief.
Also, judging by the smugness of the people I interviewed, the "We'll stop here because it's obvious you don't have the skills..." part doesn't surprise me either.