Would StarCraft be the last game AI has to beat?
After that... then we have games that involve physical movement. Although I'm not sure what would be fair for strength & speed of robots vs humans. I'm imagining a team of robot soccer players, for example.
The from playing Call of Duty to controling a robot with a gun in the real world it's a small step :)
With an AI, if we base it on pixels, what they will do is spin around 360 degrees about 60 times a second while moving forward so that it can maximize all of the pixels inputted at a time. It would compare it against the stored level design and shoot at anything that is off (or against character models). I can just see that it's not going to behave like anything we'd expect.
If you look for an RTS game, StarCraft is an obvious candidate. It has a relatively active community of AI writers and AI competitions, it's a classic of competitive play, ...
Real-time games are hard to compare, because the interface really makes a difference. Does the AI get to talk directly to the game engine? Or does it have to use screen capture, understand the image and then use a robot arm to press keys, or something in between? If it gets to see precise positions and to input commands directly, even relatively "simple" programs can do crazy micro tricks and get massive advantages that way, even if their general macro-strategy is bad. If you do the other way you need image analysis and robotics, Google should have the tech for both ;)