A couple years ago I did a workshop for CodeMash on building a portable gaming system based on the Teensy 4.1. This is an incredibly powerful microcontroller development board created by Paul Stoffregen over at PJRC. It’s powered by an NXP i.MX RT1062 crossover MCU with ARM Cortext-M7 running at 600 MHz. Despite its cutesy name, the Teensy is a little beast capable of handling a huge variety of projects, and Paul has done a great job with the ecosystem to support it.
There are also several classic gaming and computer system emulators available that will let you run games and ROMs on the Teensy. The R4ge Pro Badge brings all of the peripherals needed for a full gaming and multimedia experience into a portable form factor, including high-quality stereo audio in and out. It uses commonly-available breakout boards to simplify assembly and minimize the amount of soldering required.
The circuit board is available at PCBWay:
https://www.pcbway.com/project/shareproject/Teensy_4_1_R4ge_Pro_Mobile_Platform.html
Schematic, bill of materials, and assembly instructions are available on GitHub:
https://github.com/DigiTorus86/Teensy-R4ge-Pro/tree/master/documents
You’ll have to find and download your own ROMs, but the instructions do include a list of those that I was able to verify as working with the Teensy emulators.