In Russia, they have only 1 party left, so the party clearly doesn’t matter. In Usa, it is not an official dictator yet. In other countries with a dictatorship, I don’t know about their parties. So do you know any examples where the parties still matter?
By definition in a dictatorship, there are either no parties, or there is only one party, or the parties that are not the one the dictator belongs to are not allowed to be in actual opposition to the ruling one or attempt to become the ruling one. (That last one is the case in North Korea and was the case in East Germany for most of its history.)
NK is such an interesting case. They even have a party for North Korean Japanese voters. And with a 13% turnout across all the non-WPK parties, that’s a large amount of social influence they must wield relative to the WPK, even if they are under their control.