Such a cool concept! For anyone who didn't slog through their docs, the recommended hardware system (and the box in their product shots) is the Geekom A5 https://www.geekom.co.uk/geekom-a5-mini-pc and the 8BitDo Wireless controller https://www.8bitdo.com/ultimate-2c-wireless-controller/
Those + some SD cards and a spare evening for setup makes this a really tempting £400 project.