Do I have to consider the molecular mass of the oxygen atom or the diatomic oxygen molecule when determining the empirical formula of an iron oxide?
When determining the empirical formula of a compound, you only consider the molar mass of the element. In the compound itself, it is only the atom (or ion) that exists.

If you would assume the molar mass of dioxygen, then you would also assume, that the iron oxide is made out of iron and dioxygen molecules.

I do not know, and also do not understand, why the question states "dioxygen" as that is - in my opinion - false.