If you don’t care about playing on your TV, then a GPi Case 1 with a Raspberry Pi Zero 2 (which is about as powerful as a Raspberry Pi 3) probably makes more sense.
You can get the Raspberry Pi Compute Module 4 in a few different configurations; I’d recommend getting the one WITH wifi as it makes adding games and updating the OS much easier.
Great tip from Patrick in the video comments: “Make sure you buy the lite version of the CM4 do not buy one with emmc flash memory or you won’t be able to use a SD card you’ll be stuck using the flash memory it came with and it takes more steps on how to mount the CM4 and write recallbox or retropie. You can use the Gpi Case 2 as a IO board to flash what you want but like I said you won’t have SD card support. I learned the hard way and even tried writing a boot from SD script from the raspberry pi loader and it didn’t work. So like i said buy a lite without eMMC.”