How do these buttons work?
Notice that the top two contacts (1, 3) in your picture are not connected to the bottom two contacts (2,4).  Presumably the switch connects between those two points.

They could be surface mount membrane switches.  A membrane switch is basically two conductors separated by a thin membrane that keeps them apart until they are pressed together by an external force.  This is what is used by most devices that have flat plastic keypads, like a microwave oven.

Another possibility is that they are capacitance based, and pressing down the dome increases the capacitance, thus causing the trigger.  You might be able to figure this out by looking at the chip they are connected to.  Some MCUs have built in capacitance switch circuitry and there are also dedicated capacitance switch controllers.