You do have a King though. What would happen if the PM went to see him to form a government and they disagreed? The King is the one with armed guards, military rank and a fortress.
De facto means in fact. Given that the king does no governing no, he is not, in fact, the ruler. You may be looking for de jure, though I question even that.
If he tried, people would say no. If he insisted, he'd get tossed out on his ear.