I do not doubt that corrugated cardboard can be strong, having handled lots of particularly heavy items transported and stored in containers made from such material. Nor do I raise any concerns over a supposed fire hazzard.
Rather, there are a few issues I brought up, namely over how such a material for a case as shown is vulnerable to damp air or water, and will likely, due to the absorbent properties of paper and cardboard, wind up getting dirty quickly, and be imposible to clean. Heavy-duty boxes aren't meant to withstand frequent, hands-on use over the course of several years, but rather, to hold things together while they go on a truck or sit in a warehouse, until they're opened up and emptied.
Meanwhile, the PC case will likely absorb far more skin oils and dust in a week than said boxes will in their lifetimes. And of course, people don't store their PCs in cool, dry, climate-controlled warehouses; they put them in their bedrooms and living rooms, which are going to be higher in both temperature and humidity to accomodate the people, not the boxes. All told, I imagine you're going to wind up with the case wearing out within months. Which, as I see it, isn't as environmentally-friendly as a durable metal or plastic case, made from recycled materials as well, that can be readily cleaned with just water and elbow grease, most certainly not resorting to toxic, polluting cleaning chemicals. And chances are better that the metal or plastic cases will be in recyclable condition once their time of usefulness has passed.
I wish that people who manage to disagree with my points would actually adress what I'm saying rather than just voting my comments down. Of course, the former, as I'm aware, is infinitely easier.