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.
It depends how it's said. I would hesitate to correct the person who actually said it about whether they said it in a snarky way unless I was actually there.
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.
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.