Those overlays were one of the features that the manufacturers of the old ColecoVision video game console bragged about quite a bit. By having a controller with a numeric keypad that was designed for use with an overlay, games could be made that offered a lot of customizable functionality.
For example, the "Mouse Trap" game came with an overlay that let the user alter the maze by hitting one of three buttons to flip sections of the maze that corresponded to a color (blue, red or yellow).
The problem with overlays is that they tended to get lost. Finding a game complete with overlays for a ColecoVision or other system that used those overlays is difficult these days.