The first thing that strikes me is that the shape of the paper helmet seems not to have sharp protrusions like the ones on most polystyrene helmets. Those are known to be a serious hazard, with their tendency to snag on ground (etc.) irregularities, making them rotate and causing severe brain stem damage. That has to be a huge positive for the design.
The impact absorbing properties of crushed paper and of corrugated cardboard are well known, and I am prepared to accept the figures given, and their superiority over the dense expanded polystyrene in consumer helmets. The structure compares with professional helmets, which are made to measure and contain (AFAIK) an aluminium honeycomb structure with a very high impact absorption which protects at track racing speeds. Sadly those helmets cost more than most of our bikes do!
If this idea is shown to work and the helmets are available at a reasonable price (=< £40) I might wear one at times other than when my head's cold or I have to for an event or because of culture.
Water resistance is not an issue. There is already cardboard packaging which is treated with a wax that makes it waterproof and I'm sure bike helmets are no more difficult to protect.