There would be one God player - a dungeon-master, overlord, whatever the term may be - that controls the NPCs, "AI"-type units, as well as being in charge of using a RNG (or sites like
roll dice online, which I got from a simple search, or some other way that'd make sure there was no cheating). This player would act as the dungeon-master, controlling the way the story/scenario runs and making sure everyone is playing to his/her rules and not breaking anyone's immersion by god-modding/power-gaming/meta-gaming and other fancy RP rules.
One scenario I have that isn't a D&D scenario is playing board games like RISK, Diplomacy, Civilization, and others that use countries instead of characters, only without the board. You would lead a country and make decisions on different things, grow into a more powerful nation, perhaps invade a few other countries, and would have to use diplomacy and war to sort out your problems instead of in character-based RPs where you can just attack someone and one of you will end up either dead, mortally wounded, or badly injured.