How do old school, electromechanical elevators work?
I found a description of a similar arrangement on p. 333 of Electric Journal, Volume 9.

The relays close in series to gradually accelerate the car and to come to a smooth stop.

This truth table shows how each relay is closed as the car accelerates and decelerates up and down.

This is just for a simple elevator control that does "up", "down" and "stop".  Fancy modern elevators have pushbuttons for each floor, so there would be a more complex system, with relays operated by switches on each floor, and relays keeping themselves energized, a form of one-bit memory.