First off, yes, there are emulators that can run all those classic Atari, NES, SNES, and Sega games, but it’s far more rare to find a small computer that’s been modified to be a console that lets you play those games with an actual system controller.
The fellow that writes the petRockBlog decided to do just that when he modded his tiny Raspberry Pi PC to run SNES games. After choosing a stable Linux distribution and emulator to work from, he wrote a script for a launch menu, but he got really creative when it came to making an authentic retro input method.
Rather than simply converting a controller to USB, he built an adapter board that allow the user to connect a pair of SNES controller to the general purpose I/O pins present on the Pi; then, he made “a short C program [that] reads the states of the two controllers and passes all button presses to a virtual keyboard that is implemented with the help of the input module.”
There are more details available in his post, as well as a link to the program he wrote (SNESDev), but here’s the whole shebang in action--running the venerable MarioKart. Warning: If you grew up in the 90s, you may experience pangs of nostalgia.