This chair is unusual in that it is a cantilever chair, a traditional modernist form first pioneered by the Bauhaus. Cardboard can be very strong, but the cantilever form presents several challenges in using a paper material.
First, the entire chair is essentially in tension: the weight and force of the sitter is pulling on all three of the critical joints, at the floor, the knee, and the junction of the back and the seat. Corrugated cardboard is very strong in compression, when the force is aligned with the grain of the corrugations. However, it has very low tearing strength, especially when the force is perpendicular to the corrugations. I partially overcame this by using the hex cardboard, which is strong in all directions because it has no directional grain.
Second, there are no back legs, meaning the force has to find a path to the ground that is circuitous, winding along the seat to the front legs. The runners along the ground also have to be long enough to prevent the chair form overturning backwards when the sitter leans back. Most cardboard chairs have mass positioned directly under the sitter to add support where there is the most weight.
Last, unlike the cantilever chair featured in my other instructable, this chair only has two legs, instead of a continuous face across the front. To overcome all these structural challenges, it is key that every piece of cardboard become a unified whole. There are no continuous pieces of cardboard; the whole thing is made out of strips, as opposed to cutting out big pieces make the whole profile. The strips are not nearly as strong, and are susceptible to tear-out. The threaded rods at all the critical junctions provide pressure to overcome this tendency.