In the tech round, I was asked vague questions which don't have a definite answer and while I am answering them, the interviewers don't seem interested at all in my answers and are just looking and chatting on their laptops. Then I am asked how I would approach one of their challenges which is a huge and broad problem statement. Such questions are supposed to be a discussion but the interviewers are just staring at their screen while nodding.
I can see why they haven't been able to hire anyone for this role for over a year. And I suspect that it is because their Data Science team doesn't actually want someone. This is a classic issue when you get a team responsible for hiring their own manager. They often wouldn't want to! If they company is serious about hiring a director, they'd need to get someone else to be the hiring manager.