You seem to have misunderstood. The "required skills" in question are communications skills, not technical skills. This wasn't a technical interview with an engineering team member as they seemed to think. This was a personality/psychological examination to make sure that their personality and communications skills match up with the culture and personality at Google. Directors typically don't do the low-level, high-skill technical work at companies like Google. They need to understand it, but, first and foremost, they need to be able to communicate with people of varying technical skill levels. This Q&A process, as you called it, is completely indicative of a person's communications skills.
Let's apply your interpretation. In this case, they are evaluating the social skills of someone who will direct projects by bright engineers. They will aldo interface with management about it. There's a lot of skills involved sith associated interviewing strategies, certifications, etc that might be employed.
Instead, the interviewer asks algorithmic questions, gets great answers, explains they're not on his sheet, and rejects the person. This is the total opposite of kind of social problems an engineering lead or project manager deals with. Plus, the requirement of keep guessing until your answer matches a sheet doesnt reflect how goals or requirements are done.
If this was assessing social or management skills, then it's the worst method I've seen to assess it. It still is a horrible result.
