The system would come with an overlay that can be placed on a TV screen so you can project the game screen onto the TV screen and watch TV at the same time. Press a piece of paper against your TV screen to see what I mean. Before I released the system, I would release two development kits, one that is free and one that is expensive so people can make their own games for the system. The free development kit would come with a disclaimer that allows the company to copy some of the graphics and designs.
The controller would have two analogue sticks and a d pad. It would also be a 8 bit handheld console itself. The Bit processor would control the sound and the pixels so it would be challenging for developers to get the most out of the limited hardware. The controller would also control the projector turret if it is set to projector mode.
I imagined people finding creative ways to use the projector on the main unit, perhaps bringing a small power generator and projecting Wolfenstein 3D onto Buckingham palace at night. Nothing like playing Wolfenstein 3d on the wall of the queen's palace.