The Raspberry Pi makes an excellent game system already, but it's not exactly mobile. If you want to take it on the road with you, Adafruit has a guide to build a Game Boy-inspired game system on the cheap.
The system uses a touchscreen display, a 3D-printed case, an old SNES case, a large battery and a Raspberry Pi loaded up with all the emulators you want. It looks like a somewhat complicated system to put together, but Adafruit's guide makes it as straightforward as possible.
PiGrrl - Raspberry Pi Game Boy [Adafruit]