est joué is the correct answer. I’m not able to give you a reason why you couldn’t use a reflexive verb, but one example where se joue can be used is "Le rôle du directeur se joue facilement".

The reason you cannot use a reflexive when the object is explicitly stated is that it would cause said object to appear both as a noun and as a pronoun, which is normally considered an error of syntax.

Compare it to a phrase like "Le rôle du directeur _____ différemment de nos jours" where both the reflexive and passive voice are possible.