Well, has anyone made tic-tac-toe in DF yet? We'll start there.
But the general idea of Dwarfputers seems sound to me in vaults. Overly complex to build.
http://mkv25.net/dfma/movie-1813-tictactoev10simple
But no AI.
Whatever. Maybe I could use tacticus to lock the vault. Beat the game at that, and you win.
If we're basing a vault around games, my vote's on Pictionary.
But in all seriousness, I had an idea while reading this - you know how a 1x1 drawbridge looks the same both when it's raised as well as when it's lowered? Using this you could make effectively a 'blind' labyrinth run. Your adventurer stumbles into a large room with a labyrinth printed on the floor using two simple colours, with an obvious start and finish. They take note of this and cross the room, then descending to see... what looks like a solid block of fortifications, all the same colour. There are two types of bridges making up the labyrinth - the ones that are always raised and serve as the walls, and the ones that begin raised. To access the labyrinth, you must pull a lever to lower the bridges that look like floors, but once you're inside, you're effectively walking blind. You must try and remember the correct pathway you memorized from the floor in the room above before the timer runs out... and the bridges raise again. Squish!
For extra fun, you could make a series of paths through the labyrinth and each one goes to a different room, with different colours on the map floor highlighting your final destination and the different coloured levers cueing which to pull to start the timer... or a 'reverse' labyrinth where the 'wall' bridges lower and you need to find your way across there. You could actually do a whole lot more with a process like this, but that was the first thing that came to my head.