Are you guys assuming the cardboard is liquified with polymer and then molded?
Check out the video here
. I don't think he's building it they way you think he's building it.
I saw the video, but thanks for linking. The "waterproof resin" mentioned in your link is the polymer that we're talking about - it's sprayed/spread on the complete cardboard bike part (a laminate of corrugated cardboard). Like with carbon fiber, this resin matrix is key to the rigidity and durability of the final product.
In the video, around 2:15, the inventor is applying an early iteration of this polymer. Doesn't look like a very eco-friendly process in that stage of development! There are probably better/cleaner polymer resins out there, so I'll give him a break on this one.