How the interviewee is supposed to even guess this is an OOP question, as opposed to a "solve this problem" question? Unless the interviewer goes out of his way to mandate an OOP solution, he will just get whatever is the best guess of the interviewee.

In my case, this is unlikely to yield an OOP solution. I'm even less likely to guess an OOP solution was even expected. And if I fail the interview because this particular company takes OOP for granted, I should fail the interview, and may even be glad I did.

It does not mention how the question was put, and in which context. If it was clear from the start that the OP was expected to use OO, then it would not be smart to start with the bitboard implementation and then continue to argue about it. ... But if the question simply was, "how would you design a chess game", with no other context, then it would be reasonable to assume that the interviewer would want to hear your best solution... and for that he chose the non-OO bitboard version, based on his previous experience with chess engines.