Why are the military interested in Hexayurts?
The short answer is that the military is always looking for new ways to solve problems.
The long answer is more complicated.
The Long Answer
Firstly, the role of the military changes over time. The basic job might be pretty well understood, but very little of the complexity of the military can be explained by the simple need to fight and win wars. In fact, it is dealing with the unknown that makes the military so complicated. Right now, if something totally out of hand happened, like aliens or a giant meteor or a Godzilla attack, the military are the people who get the call. It's their job to protect against the unexpected, against all threats both known and unknown, and to - if necessary - give their lives for that purpose.
You're reading this page over the Internet. The Internet spun off from ARPANET. Why did the military build ARPANET? Well, at the time, it didn't have direct applications. It was a capability that might be useful in the future.
It sure is.
Things are changing at the Pentagon. In 2005, Gordon England signed 3000.05 which says that the military has to develop really advanced capabilities in fixing things up, and that they should get about as good at fixing things as they current are at breaking them. To be more precise, it says:
Stability operations are a core U.S. military mission that the Department of Defense shall be prepared to conduct and support. They shall be given priority comparable to combat operations and be explicitly addressed and integrated across all DoD activities including doctrine, organizations, training, education, exercises, materiel, leadership, personnel, facilities, and planning.
Stability operations are conducted to help establish order that advances U.S. interests and values. The immediate goal often is to provide the local populace with security, restore essential services, and meet humanitarian needs. The long-term goal is to help develop indigenous capacity for securing essential services, a viable market economy, rule of law, democratic institutions, and a robust civil society. (emphasis added)
So within that mandate, there's a whole new generation of research and thinking about how to take care of people as if it was as important as blowing them up. Yes, there's a clear mandate that this is done in a way which promotes US interests. This is the Pentagon, not an Ashram. People want something in return for their tax dollars. US interests means "keeps the voter happy." The government defines US interests and there is much scope for refinement of the current definition.
I believe what's going to come out of this directive in the long run is Internet-class solutions for shelter, for housing in general, for power, for water, for lighting, for cooking, and for every needful thing.
The Internet had uses beyond those originally foreseen by the military. They will solve these problems in the context of their mandate, which includes an explicit national agenda, but the technology will be portable to every village, every slum, every farm - just as the Internet is spreading all over the planet.
Nobody else has the global mandate, the funding, or the mission.
The Hexayurt is a little start. It's part of a much wider picture of development. So don't knock these guys. They brought you the internet, and they're doing the best they can.