So you would like to build your own tiny game console? There are already plenty of guides and tips available around that show you how to do that. You can also buy what others have made to complete the project faster. Take the PiBoy Nano for instance: it is a 3D printed game console powered by Raspberry Pi.
PiBoy Nano is similar to the PiGrrl, which we covered here a while ago, but smaller. Simply buy the electronic components from Adafruit and other retailers, and you are set.