In a conventionally built PC, the case, made mostly from one kind of sheet metal, is quite easy to recycle and can often survive the mainboard and CPU, so replacing it with cardboard is not that much of an improvement.
It looks funny, though.
You've obviously never cut your hands to shreds working on cheap metal cases repairing peoples PCs.
While it's quite cool.... the first time you spill a beverage on your desk and you PC case dissolves I think you may regret buying a cardboard case.
I made a cardboard PC case my freshmen year in college. It did catch fire...
This is sort of cool. But, on second thought, and regardless if normal operation temperatures are safe with a paper case - I dread the thought of a abnormal occurrence with any one component shorting out. That could cause a fire, and for the chance of that happening, I wouldn't think it wise to use a case like this. Components fail, it's a fact of life - I won't up my risks with this.
I just wanted to say that the creator of the project is a great guy. He has spoken at the Houston HackeSpace (http://txrxlabs.org). He also gave a great talk at Entrepreneur Camp Houston (http://entrepreneurcamp.pbworks.com/) about lessons learned from his startup.
Without the cardboard case the $874.99 PC (no OS included) costs $340 in parts from Newegg.
That's one hell of a markup.