So, after giving it a bit of thought a couple ideas of how this could be used come to mind.
The first is something of a competitive manner, akin to the game Illuminati where everyone is playing a secret (or not so secret) organization vying for control and attempting to fufill some set of goals affecting the world (hide the presence of aliens, become secret masters of the world, attain techno-occult transcendence, etc. ) while preventing anyone else from doing so.
Another option is more cooperative in that each player still controls an organization or small country but they all have a common opponent in some other gm controled faction such as an alien invasion or massive expasionistic empire.
One further option which could work with either of the earlier options is that the players are avatars of some sort, essentially giant monsters or perhaps something like fledgeling titans finally let loose on an existing world to make their mark on it (perhaps something akin to the concept behind "Lunar Quest"
Either way, the players could then use their abilities to essentially create assets, organizations and characters that function mechanically as sub characters for each player. Perhaps under varying degrees of direct control by them
