What is this foam ribbon cable alternative in an old Norstar set?
It's called an Elastomeric Connector.  They are made with alternating insulating/conductive regions, side-to-side, so that they conduct only in the vertical direction.

Matching pads on the board contact the conductive parts of the elastomeric block.  Compressing the block between the boards compresses the surface to the contacts on the boards and makes a board-to-board connection.

The plastic shell makes sure that the connector does not buckle when the block is compressed.



(From http://www.zaxisconnector.com/images/Elastomeric-Connector-Collage-Compressed.jpg)