As some of the other posters have pointed out, the car in the photo definitely appears to have rubber-in-tension (probably bungee chord) suspension. The 'mystery box' is the pulley block for a number of rubber bands in parallel. The pullrod is adjustable for length to set the ride height (and to keep it, as the rubber probably stretches with use and age).
What appears to be a drive shaft is merely the track rod - you can see the grease nipples for the ball joint at its outboard end. The bit that isn't steering or wishbones is probably the brake hose as someone else also pointed out.
The telescopic damper and its gaiter also looks interesting.
But it's not the very same car depicted in full on 500.org...
