If I compare the pictures of the add with that of the original flyer, it looks like the joysticks shaf and balltops are missing.
The shiny "balls" you see seem to have a black ball-top joystick on top on the flyer. A weird joystick construction indeed. I zoomed in a bit on that flyer and those shiny metal things actualy look a bit like a metal ashtray, with indeed a joystick shaft and black ball-top in the middle........they sure match the Atari startbuttons nicely !