Everytime I have been invited to a 1 on 1 with someone high up the org ladder, I have been given talking points from the people in between
Especially from someone new to the field these are questions I would be expecting, especially at a tech company (so pretty equalitarian and meritocratic where the director probably started as an engineer himself). I would also expect the career path to take to get into management to be discussed as well.
But the question itself doesn't strike me as such, at least coming from a junior engineer.
Someone more senior should know what the tasks of someone at that level are, so asking "what is your job" might be interpreted as implying he isn't doing much.
And, I've worked in places where you are free to send a DM to the C-Suite if you feel like it's necessary to get your work done. No pre-approval required.