At first I thought this was silly since I just re-use cases until they fall apart, but then I realized that a lot of people are probably buying full desktops.

Now if only the chemicals used in manufacturing chips and boards weren't the most incredibly, dangerously toxic chemicals in the world, we'd be ok

I may not have gone to university for engineering, but I do know retail electronics need an EMI shield.
You could get away with selling it to the DIY market, but it's not a big enough market to really make a difference that this guy is talking about in the video. He could add simple tinfoil like in an iMac though.

However the real problem is that an electrical fire could ignite the case. That's not even that rare in computers either. Once you factor in houses burning down I think the metal cases will turn out to be much "greener".

^I think you missed his point: it's not about marketing cardboard computers, but illustrating that smart and sustainable design can replace the lazy and wasteful use of prime materials.