If I remember correctly, the tweel was initially developed for military applications. After enough complaints (and lost lives) from getting flat tires in the middle of battle, Michelin was enlisted to create a tire that was non-pneumatic and resistant to damage. The result was the tweel.
As with most technology developed for the military, we can expect adaptations for use in the civilian sector, eventually. One thing I wonder about, though; how would you "air" them down for off-road use? I imagine with such a stiff "tweel," you'd get bounced all over the place going through the rough stuff and would potentially run into traction issues.