It works the same way as a glider wing.
A wing makes lift roughly 90 degrees to the incoming air ( a little more than
90 based on the L/D of the airfoil).
In an autogyro (or a glider) the incoming air is coming from slightly below
level, 15 degrees. This makes the lift vector tilt a little forward of vertical, causing
the blade (or wing) to go foward.
Your car example has the incoming air dead level, not the same.

Try here for diagrams, etc:
http://www.jefflewis.net/autogyros.html
http://www.copters.com/aero/autorotation.html
http://www.autogyro.com/technic/jeflewis.htm