I'm also interested to see if it can be done.
Eve has a collaborative narrative.
Soul Caliber has visible numbers on weapon upgrades, and does have a narrative.
Gran Turismo has a lot of visible numbers.
Battlefield 2 has a loose narrative, but it is a strictly multiplayer game.
You cannot see your weapon damage numbers in quake, but you can get temporary upgrades to your armor and health that are displayed numerically. It also has a narrative.
And I'm totally serious about the reward- I'll even see if I can't get someone else to judge so that it's fair.
Soul Calibur, Quake and most if not all action games don't have directional stat growth in the same way Final Fantasy or BG have.
I think my definition of an RPG as a game where there is directional, visible stat growth for the player avatar, and where the game has a narrative includes all games in the RPG list, and excludes all games in the second list except for Warcraft 3. However, it could be argued that the units controlled by the player inWarcraft 3 are not player avatars, and as such I'm going to exclude it on that basis.