As a experienced Civ player (I discovered Civ 2
way before F2) I can tell you that somebody actually made a Fallout-themed scenario for Civ 3 eons ago. It did play quite well, but I lost it when my old hard drive went to electronic heaven. I went to the trouble to find the thread...ain't I nice...
http://forums.civfanatics.com/showthread.php?t=199196
I could see a game in which you're in a Vault...somewhere which Vault-Tek decided that the vault would have critical failures of...everything after five years of operation. They deliberatly put in the posistions of command dominant people who would clash with each other as soon as problems cropped up...
You're head of a squad of people who have been sent out to get a part, and then the story forks out from there, depending on what desicions you make in the first mission (like if you used force or diplomacy to gain your goal.) I'd see a situation where you'd have the squad-based out in the wastes, but solo inside the vault.
With the different leaders forming factions inside the vault, each will try to sway you their idea on what has to be done for their survival, and ask you to do the main missions in a particular way to further their goal. You'd also be able to wander around the vault, talking to the other people and perhaps get a few mini-quests.
I'd introduce the idea of time passing - like at each end of the 'world', you're given a mission which involves travelling for months, so when you get back the vault has changed depending on the choices you made earlier (like if you repeatedly chose 'force', you find that the security units have become a standing army.) I'd make it that there are a dozen or-so endings ranging from a neo-fascist police state to a rising feudal commonweath.
I'd call that a spinoff, not a Fallout-themed other game.