A few years ago, th solar impulse people wre talking with my university about potential cooperation. I'm not sure if anything came from it, but in the meantime we did a student project making a rough design for such an aircraft. The Solar impulse manager already mentioned our design had very similar parameters to what they were thinking of, and indeed, the numbers you mention here sound familiar. ( I guess I am a bit proud of that)

So assuming this design is somewhat similar to ours in more respects than just these numbers, I can make some educated guesses on the project.

Our design needed a lot of batteries, something like 40% of total weight if I remember correct. That means   you have even less weight to build the wing. In fact we gave the aircraft a 'gravity battery', letting it climbs 10 kilometer during the day while gliding downwards at night. The high altitudes their site mentions suggest they have similar plans, but I am not sure about that. ( they might also just fly high to go faster).

As their site mentions, you will need wings made of only a few tenth of a millimeter material thickness.
The main reason you can do this is that the wing is mostly carrying itself. In a normal aircraft, the wing produces lift that counteracts the weight of the fuselage, so there is a distance between the application of the load and the lift force. This creates a bending effect that is usually the heaviest load on the structure.

However, in this design most of the weight is in the wings themselves, and the solar panels on top and the batteries divided in it. In a sense, you can imagine a short-winged aircraft whose wings are carrying the fuselage, and then add extra wing at the tips that only carries itself and the solar panels on top. If you look at the Helios unmanned aircraft, it had the same effect even stronger ( it didn't have a fuselage at all).

In the exercise, we had to assume very positive figures to make it work at all ( that is, extremely strong and stiff materials, the best solar panels and batteries, the best engines, extremely tuned aerodynamics). My personal opinion was that we had no margin at all left, and therefore really not a viable design.

So, I am really looking forward to see if they can make this work. It would definitly stretch the limits of what is possible.