OWI Robot Arm Circuit Diagram LED question
The question now is does the drawing match the robot.

The drawing is definitely wrong. 

I am willing to bet the LED is installed in the robot the opposite as in the drawing.  It is easy for someone to draw the diode backwards.  But if the LED never worked then someone would have noticed. 

If you flip the switch one way the LED should be on, the other way off.  Or visa versa. 

I am guessing your LED does not light up no matter which position the switch is in.  This means either the battery is dead or the LED is dead. 

Connect a DC volt meter between pins * and -, if it reads 6V then the LED is dead.  

I am guessing it will not read 6V but rather something like zero or close to it.  

LEDs last forever and rarely die if not abused. Batteries will die, it not a matter of IF they will die, it's a matter of when they will die.