One reason for the lunch is to try and relax a bit and test “cultural fit”, which is more like a blind date between two people to see if there is any spark. Ideally it is a two way conversation, where the candidate and the interviewers get to judge each other.
There is a problem where cultural fit “tests” are heavily biased against minorities - for example most any sports discussion is dominated by your social class.
Enjoying brain teasers matches a particular type of geek, and the discussion likely veered or was encouraged in that direction by the candidate. It wasn’t Machiavellian, which perhaps you are more responsive to?
TBH I'd just have found it contrived and boring. I wouldn't be excited to have colleagues who couldn't just talk about normal stuff at lunch.