In my _expert_ opinion I don't think the choice of optocoupler matters much here - I think pretty much any device with a compatible footprint will work.
Here's the internal schematic of the PC814:

The back-to-back diodes on the input means it is designed for AC signals - not for a DC control signal that your schematic shows. That said, I would hazard to guess that the PC814 in all likelihood will work fine in this circuit.
I would try any one of the 4-pin optocouplers on this page specified for DC input:
https://www.jameco.com/shop/keyword=Optocoupler-4-PinSince you already have a pcb, just make sure the pinout and footprint match.
The hackaday.io project seems to be here:
https://hackaday.io/project/94791-retro-cm3-a-powerful-retropie-handled-game-consolIf anyone has Altium there is a PCBDOC file available there. Perhaps it has a BOM?
Update: Just noticed from the photos that the board uses SMD components. So it would be a good idea to get the footprint and pin assignments from the PCBDOC file.