How is this circuit detecting the LED?
the question is how the microcontroller (unrelated to my Arduino) in the cruise control system is detecting the existence of the LED?

The diagram you provided implies this is an external board that connects via a connector board and probably other components to the microcontroller.
Now, there a few methods to detect whether or not a component is connected to the circuit

mechanical sensing
voltage sensing
current sensing

Let's say it's a mechanical sensing, if you remove the module there's no way to tell if it's the module missing or just the led. So this is ruled out.
Voltage sensing and current sensing, seem more likely not because of logical assumption, but because, among other industries, automotive industry also uses these techniques.
EDIT:
On the mechanical part you can have 2 mechanical switches, one to detect if the module is plugged and another one to detect if the LED is present. However, this method does not assure that the LED can provide a path for free electrons to flow aka conduct electricity.