Not sure how the rear wheel won't be getting sheared off. Same with those cranks -- a single bolt like that for each arm looks like it wouldn't be tight enough. And that bottom bracket doesn't look terribly serviceable.
Where's the front brake?
What happens when a sideways pressure is applied to either wheel?
How much weight will end up being added to the frame and wheels in order to keep them stiff? Removing tubes from the normal diamond frame design mean you need to make up for the support they provided elsewhere.
Some group of students actually built a bike similar to this and posted it on Reddit in 2009 or so.
What I never understand is how people imagine the drive on the rear wheel. You'd need an impossible gearbox to spin the gear that interfaces with the rim, and even that gear would need to spin like 10 times for every revolution of the wheel.
To me, that kills the fantasy so thoroughly that it isn't even fun to look at a picture of the device and imagine it in perfect world scenarios.