As much as I like Apocalypse World (and its many spin-offs like Dungeon World), it is still a Game About Stats. It is one of the most focused Games About Stats that I have seen in a long time; it doesn't matter what the other person's skill is, if you succeed lives on your stats alone. This keeps the game rules part more understandable and accessible. Mind you, all the AW games are pretty damn dark.
One of the best Games About Not Having Stats is Polaris, but it's only for three players. Its system is really nice in that only certain people are allowed to tell certain aspect in the story.
If you like that idea, then Microscope may be your game, as a structured world-building exercise. It's the game I want to play to set up a Mu*'s background.
I like character generation in Fate Core, you're tricked into playing an RPG system because it looks like a cooperative story-writing exercise, but after that it becomes a Game About Stats.
The classic and venerated Prime Time Adventures is another game that tricks you into playing an RPG and can be presented as pretty much a party game. I feel that it can be simplified even more than the manual. It's been Kickstarted for an update, and I hope that comes out soon.
I'll echo RDC's Don't Rest Your Head as being a stats-light game, but it's also very damn dark, and it has a lot of (die) resource management to it. It has a very board-game feel to it.