You need to turn the Regicide option off.
In a regicide game, any city taken wins the game.
Note: I have never played this mode, but I know it exists. I may have gotten the name wrong, I know there is a regicide, and I'm gussing that's the option you left on. Whatever it is, it will be on the initial screen when you start a game and select the rules (such as capture the princess, accelerated production, etc).