It looks like that controller has a reasonably decent CPU and graphics hardware on it. Given the camera and other hardware on the unit, it is very likely that the device is locally executing some program to interact with the main console. It isn't really that practical to render everything on the console and stream it uncompressed to four separate tablet remotes, so I think this is the likely implementation. If this controller had some form of local storage or even an SD card slot, it could hypothetically be used as a standalone "Nintendo tablet." This would involve Nintendo competing against itself in the handheld gaming market, but if the controller has high enough specs, it might be a good hedge against the 3DS catastrophically failing against the new Playstation Vita. While the device could obviously not directly compete with iOS and Android devices, it could fill an important niche role, especially if Nintendo could market the device as a safe tablet for children. With the right apps, they could even sell the things to schools.
