I think that is really cool.
Without the tread, I can see it being used on off roads and way off roads like on a distant planet where it could be adjusted to different terrain.
I think it would be great for vehicles without a spare since it seems to not be filled with air.

The main problem I see with this for an off-road application is that the times you need to reduce tyre pressure, and use that extra width, are the same times you need extra clearance. All pictures here show the diameter decreasing as width increases, so the clearance would drop with a width increase and you'd still be stuck, probably more so.

I like it a lot but vehicle will have to be light and slow. Acceleration & deceleration forces will rack the unsupported elements over.

It will be interesting to see if this goes anywhere. One of the reasons pnuematic tires have persisted is that it is difficult to create a material that can flex without failing as often as tires demand yet still offers impact absorption. If he can solve those two problems he will have beaten a number of major companies.
See: http://www.michelintweel.com/ http://www.gizmag.com/reinventing-the-wheel--the-airless-tire/10398/

I don't see it making a smooth rolling tire.

wouldn't the reduction in circumference lower the vehicle too much and let it get hung on rocks and such when in off road mode?

It is an idea. One that will, unfortunately, not transmit torque.

This is going to run into the problem of what ever elastomeric covering they use for the tread is going to wear down very fast. The types of rubber that allow for a lot of stretching are also the types that show poor wear characteristics.

Very clever concept. Now it's time for the materials research which will be a major challenge.

A ridiculous throwback with few, if any, real world applications. If successful, this design will require pneumatic suspension to maintain/adjust ride height and open wheel chassis and/or axles that telescope. It will never have high speed capability and as for cornering...forget it. Maybe as a snow machine or bush and swamp buggy.