There is just about zero info on that coin mech.
Try connecting it to a 12V supply and temporarily connect an LED and resistor between +12V and the NO contact.
Set the speed switch to slow.
If that gives a flash when a valid coin is put through it, the NO output is being switched to 0V
If the LED does not light, it may be giving a 12V pulse rather than grounding the pin; try the LED and resistor between NO a ground?
The USB adapter board feeds +5V to the outer pin on each connector, so a relay or optocoupler would be needed to convert the 12V pulse to a separate contact that can connect to the adapter.
Whichever circuit works with the LED, connect the opto relay input, pin 1 to the positive side and with a series resistor (same as for the LED, to give 5 to 10 mA) to set the opto LED current.