The circle pad consists of a small, donut-ish PCB with traces, a backing plate, and the spring-loaded X-Y sliders.

The X-Y sliders each have two metal contacts that are always touching the PCB.

As you move the sliders up/down and left/right, the metal contacts are adjusting the resistance of the circuit on the PCB.

This, in turn, is registered as movement in whatever game you're playing.

Regarding the spring-loaded sliders: A spring inside the mechanism makes the "stick" always return to center. If you wanted to convert the circle pad to more of a "throttle" type joystick — where it doesn't return to center automatically — all you would have to do is take the circle pad apart and remove the spring found within.