AVR Pin change interrupt: Capacitive Touch Sensor
You have to remember that this is a capacitive touch sensor, depicted in the circuit diagram as a standard capacitor with an annotation. The users finger is an implied part of the operation of the circuit.

There are a few ways to implement it, the most basic is that the sensor only including the bottom plate of the capacitor. When the users sticks their thumb on the top of the capacitor the thumb forms the top plate.

So when the capacitor is incomplete, the voltage is high. When the capacitor is completed by the thumb the voltage drops low, in practice the thumb won't build charge, so it will stay low.

The delay counting is a noise rejection setup, this is similar to a normal physical button debounce, but worse as the system is rather noise sensitive.