So I'm noticing something now that I didn't know before.
I had the ATX PSU plugged into another outlet and was testing it that way. I would turn the ATX PSU on (with the switch, but it didn't actually "turn on" until I turn the arcade game on) and it would be in standby mode and I saw no LED coming on.
I now have it hooked to the arcade PSU and the "switch gets flipped" when the arcade turns on, and then the ATX PSU also "turns on" when it starts up. And I'm now seeing the LED flash quickly initially. But if I turn the game off and back on, the LED doesn't flash at all.
Also, the game isn't turning on. The LED is staying on really short, like shorter than it was with the circuit 1 before it started pulsing.
I'm just about giving up on this and feel defeated lol. I think the first circuit was closer because it was actually doing the job, but it like kept trying to do it and that is why it was pulsing I believe (coudl be wrong about that). It also seems like the cap is not discharing on circuit 2 like it was on the first one because when I try stuff a second time, the LED doesn't come on which I'm guessing is because cap isn't discharged yet.
Adding an extra resistor just now in line made no difference. So it's now going PWRPin -> resistor -> resistor -> XOR1 and it's the same as it was before without the extra resistor.