The density likely leaves out the weight of the air filling most of the volume, and just represents the mass of the metal divided by the structure's volume. This is reasonable, given that the air plays no role in the structure's stability or strength. It could just as easily be in a vacuum, or in some other gas. You can't say the same of the frozen smoke linked in the article, as air forms an integral part of its structure.
I would think it's about the "apparent weight" i.e. including the buoyancy in air. So it's density would be 1.2+0.9= 2.1mg/cm^3. Also they count the whole cm^3 which is 99.99% air and only 0.01% solid...
So, basically, it would be ideal for building a zeppelin. Put a bunch of it into a container, and evacuate it to go up. Fill the container with air again to go down. Nothing flammable to explode.
Of course, if this could be used for large portions of the structure, that really changes the equations a lot. You don't need nearly as much lift for a given weight of cargo.
The Hindenburg used 200,000m^3 of hydrogen (generating a lifting force of approx. 215,000kg. Net useful load was only 10,000kg.
When selecting materials for building aircraft weight is only one of many concerns. Durability, flexibility, strength, cost, etc are all major issues. Considering the design goals for this material seem to primarily just be weight I would be surprised if it's strength to weight ratio was impressive enough to overcome cost issues.
Also compared to a modern blimp the Hindenburg an ancient design that's been far surpassed. A modern Zeppelin is much closer to 20% lift to weight ratio than 5 for the Hindenburg despite using less efficient helium gas. Their maximum permitted takeoff weight is 10,690 kg, with a payload of 1,900 kg.(http://en.wikipedia.org/wiki/Zeppelin_NT)
Strength is the key part they didn't mention. DARPA probably wants that bit for themselves :) However one must assume this has some strength, otherwise what would the point be. Very cool stuff
DARPA might well be funding the research for the possibility of a future alternative to FOGBANK in nuclear weapons, which isn't as dangerous to produce.
1. http://pdg.lbl.gov/2007/reviews/atomicrpp.pdf