Let's take your favorite dungeon crawl game as an example. Rather than telling a story about adventurers in a dungeon, we're going to tell a story about a group of politicians on the campaign trail. We'll call this game Demi-Humans & Democracy. Imagine that the rules work exactly the same, but that we may rename certain terms so that they describe different events in the fiction.
Rather than hit points, our game has support points. If you reduce a target to 0 support points, you don't kill it, you turn it into a contributor to your campaign. The treasure that you would normally receive from killing a monster instead represents money they donate to you.
Rather than ranged and melee attacks, our game has speeches and conversations. Speeches take place over a distance, and conversations happen within about 5 feet. NPCs respond with objections (ranged) and complaints (melee) that function just like speeches and conversations. Use whichever term makes more sense in the fiction.
Rather than bows and swords, you use megaphones and wristwatches. Depending upon the dungeon crawl game you use as your base, you may end up with a +1 Mighty megaphone or a dragonbane wristwatch. Likewise, you don't use armor, but there a variety of business suits that are statistically identical.
Do you get where I'm going with this? There are some other things we would have to rename, like stats, saving throws, and some spells. But we could probably leave skills nearly unchanged, assuming your political game happens in a fantasy Mideival setting.
You may initially think that there would be some problems separating Charisma skills and combat rules, but as long as you are clear that charisma gives you volunteers and speeches and conversations give you financial contributions to your campaign, I don't really think there will be a problem with the fictional balance of the game.
So what do you think? Do you like this sample of hacking the fiction but leaving rules as written? What better example would you like to try? Let me know. You can find me on Google+ or on Twitter as @joshtjordan.
Image by vintagedept. Used by permission.