How do Dualshock 4 pressure sensitive buttons work?
It has the apearance of a force sensitive resistor, the (lower) conductive dome behind the button squashes, progressivley bridging more and more of the resistive stripe (black rectangle) as the force is increased.  Thus the harder you press the lower the resistance.

There will be some sort of analogue to digital, but I can't see what sort they are using. but given that the description says "voltage divider output" that suggest that the resistive button is used in a voltage divider and that the output is sensed with a voltage sensing ADC, probably built into the microcontroller tha runs the gamepad.