While its not quite what you want (uses a DC barrel connector instead of USB-C) this is basically the same thing?
A hobbyist in Japan made a supergun powered by USB-PD:
https://j-7system.blog.ss-blog.jp/2022-03-09
It features DualShock 4 controller support via Bluetooth and a custom FPGA-based sync separator to convert the video signal to RGBHV. With built in S-video and Composite outputs as well.
Hooked up to a small 15kHz RGB compatible LCD monitor with everything running off a 45W power bank. The USB port next to the barrel jack is for powering the display.
Video:
https://twitter.com/s_osafune/status/1500481170920046592
Apparently it can only run for up to 2-3 hours per charge. But a "real hardware" arcade setup as minimal/portable as that is still impressive!