I don't think your story even has to be based on a game. It is probably easier to write a story that is based on a game, but I don't think its necessary. But if you do base it on a game don't do it as an AAR is all, i.e. 1 or 2 events that happened to one character in one of your games is probably enough to fill out a 5,000 word story.
Quite right. You can certainly use a game as inspiration for your story, but you do not need to base your story on a particular game of CK2. You are free to make up any story you like that you think has a CK2 feel to it (and is set in the CK2 era).