What is very interesting is that it utilizes a hybrid air gun / gun powder system. It uses a gunpowder charge to accelerate a piston which compresses hydrogen gas to 100,000 psi (maximum pressure of a .338 Lapua Magnum is 60,916 psi). This propels a saboted projectile at 26,400 fps!

The piston system if very common. All spring air guns use it, even the simple springer airsoft guns use a simple piston system. The difference is they use a spring to propel the piston which compresses air.

Here is my attempt at explaining my understanding of how the NASA gun works:

Excuse my drawing skills. Click to expand

UPDATE: A diagram by NASA of a Light Gas Gun (thanks to R.A.W and Billl):

I got it more or less correct