In this video from Pi My Life Up you’ll learn how to install and use software called RetroPie on a Raspberry Pi. RetroPie lets you emulate a bunch of different game platforms, like Atari 2600, Sega Genesis, Game Boy, and so on.
By the way, I co-wrote a book with Ryan Bates called Raspberry Pi Retro Gaming: Build Consoles and Arcade Cabinets to Play Your Favorite Classic Games, which has instructions for building a tabletop arcade machine.