Oh, I'm glad you picked this, it's one of my favorites too, found it years ago! If I remember correctly it wasn't written as fan fic per se, that's why there's no names, though it's very clear who the characters are. It was part of a short story collection.

I like the structure of it, the way the word game takes you deeper into their games--as we find out what they do and who they are. Really good characterizations too.