The pictures below show the insides of a Williams Expo game illustrating the "circuit board" sometimes called the "relay board." Components are mounted to a piece of plywood that rests on the bottom of the cabinet resembling the way components are layed out on a circuit board in modern Electronic games. The main difference is that these components are electro-mechanical devices such as switch stacks, solenoids, and a motor with switch stacks mounted around it (score motor). The score motor in this case is the round looking device in the center of the picture. Note the various switch stacks that are mounted to it. The center shaft turns causing switches to open and close. Kind of like lobes on a camshaft.
(click any picture to enlarge)