In recent days, we've written about Arm-based portable retro-gaming consoles running Linux or Android with products such as ODROID-Go Super and KT R1. The former is affordable at $80, but people may complain about performance, while the latter is much more powerful, but is expected to cost around $200.
If you'd like a rather powerful portable retro-gaming console, but don't plan to spend more than the $80 asked for Odroid-Go Super, you could always connect your smartphone to GameSir x2 gamepad/game controller that brings most of the same buttons and joysticks through the USB-C port of your phone