The device is just the monitor panel itself; it is showing you the 12V system voltage (at a very, very coarse resolution). All the circuitry required is in the monitor panel circuit board itself.
Basically, the bottom LED illuminates whenever the check switch is pressed and gives you absolutely no useful information other than perhaps that you do indeed have 12V power. The remaining three lights illuminate when the system is over some preset voltage, as detected by a simple comparator circuit in the display unit. I have not sketched out a schematic of mine to see what it uses as a reference voltage--maybe there's a zener diode or something similar, or maybe even the forward voltage of the always illuminated bottommost LED.
There's no purpose-built ADC or microcontroller or anything at all sophisticated in most of these sorts of panels...though, these days, a little microcontroller would probably be cheaper if one were designing the system anew from scratch. Something like an ATTiny404, currently available for $.55 in single quantities from DigiKey, could easily run one of these monitor panels with four or so things monitored with minimal external components (a voltage regulator, some resistors and LEDs, a switch).