Gragh.
Ignoring the above, some kind of MMORTS.
You're given a patch of floating land in the sky/space, you start to build a city on your patch of land, but space quickly runs out, so you pack some citizens into a colony ship and drop them off on a new patch of land, and they build a second city.
This goes on for awhile, untill you come across another civilisation, interested in the very piece of floating land you are.
So you draft a military, and attempt to sieze the island. A war breaks out, with battles taking place not only on that island, but with raids on established cities in an attempt to cut off enemy supplies.
However, the islands are deformed by war, explosions chip away at the already small mass, and eventually the land is too small and uninhabitable to bother fighting over.
The deformation encourages diplomacy, where players make agreements with each other to avoid completly decimating each other.
To balance out the "lets all share" mindset and encourage acquiring more land, the player's civilization is constantly growing in population, so you need to continue to grow to fit all the new citizens. Eventually, it will stop growing noticably once you have around 40 islands worth of people.
The only problem I can see is people getting attaked and defeated while they're logged off. A possible solution is giving players the ability to build expensive, high tier shield generators which activate for the island they are on once the player logs off.
As for actual gameplay, the main focus centers around four ship types:
Colonization Ships carry a group of twenty or so civilans and some resources.
Landing a colonization ship on an uninhabited part of an island will start a colony on that island. Each island starts off with only a bunker which people live in, and resources are localized to each island.
Trade Ships aren't directly controlled by the player, they determine which action will earn them the most profit, either through buying and selling goods, or transporting civilians. Trading Ships come into existence on their own, and the larger your cities are, the more ships which will base temselves there.
To get resources for building and expansion from your existing colonies to new ones, the most efficient way is to offer government incentives to trade ships, "Extra Bonuses" or tax cuts when certain goods go to certain places.
Military Ships have no weapons themselves, they serve as transports for infantry units, landing them down on potentially hostile territory in an attempt to sieze an area before colonization.
War Ships are ships build with the intention of fighting, some are better suited for taking on enemy ships, some are for taking out ground locations, and some provide misc. support, like radar jamming or EMP flashes.
...That had waaaaaay more detail than I intended.