You can already find real bikes for $20 in parts of the world like China. Since the article doesn't say so, I guess that this bike has to be quite a bit cheaper to make than $20 for it to be worthwhile, but then it'll be the labor costs that outweigh the material costs by far.
Metals are much easier to recycle than paper products.
To recycle metals you might need to do a bit of pre-processing, grind up everything a bit, and throw it in a crucible to melt it down. 100% recyclable and the same as new when recast.
To recycle paper you have to make sure everything is sorted (no plastic, metal, etc in with your paper) and do a good amount of chemical processing and the end result isn't as easily like "new" paper.
I don't see how this gives cardboard the edge in recycled materials use for a bike.
While metal recycling might be simpler in terms of the process, paper recycling might still be more efficient in terms of energy/volume or money/volume.
Energy used for recycling paper: roughly 1000 kWh/short ton (Wikipedia). Savings of about 60%.
Energy used for recycling aluminum: 700 kWh/short ton. (Various websites.) Savings of about 95%!
I knew aluminum recycling was crazy efficient compared to refining it in the first place, but I'm surprised it's the same or even cheaper per ton as paper.
Sidenote: Recycling aluminum really makes sense when you consider the energy you need to make it in the first place:
"Large, modern cells operate with a specific energy consumption of 5.9 to 6.4 kWh/lb of aluminum. The energy required to produce aluminum from scrap metal is approximately 5% of that required for primary production"
