I rather suspect that this is a bit of nonsense concocted to gain publicity. Firstly corrugated cardboard is a dreadful material iff the intention is to keep components cool. By the standard of these things, it's a fairly good insulator. Indeed it's a choice of last resort for the homeless. Secondly, what about electromagnetic interference shielding (unless, like plastic cases, they are using a metallic coating). Thirdly, most desktop cases are metal which is much more robust, perfectly re-usable and much safer. Fourthly a corrugated cardboard case is not much protection for delicate electronics, either in purely mechanical terms or from accidentally coming into contact with quite small amounts of liquid. Fifth, just how much of the energy content and engineering effort goes into the construction of a PC case rather than its inards, power supply and so on? Given the lack of expandability of this thing for disk bays and so on, then what's the point of the desktop format? Stick to something like a Shuttle - smaller, neater, more robust and, I would suspect, ultimately more "sustainable".
Nope - I think this is just somebody seeking some publicity which, reading around the Internet, many tech news websites appear to have fallen for.