Using an Arduino as an LED controller for an arcade stick
I think the idea of putting the arduino between the button and ground is the problem here — 1P appears to be the input for the controller button, and you can't expect to take an 'input' from the button on both pins at once.

Try connecting one lead of the button back to its ground, and the other to 1P (as it would be originally I assume). Then solder/connect another lead from the button's non-grounded pin to an arduino pin designated as INPUT_PULLUP.

This way you have two pulled-up input pins connected to the same button pin, which are both pulled low (since Arduino &amp; PS360+ share GND) when the button is pressed.