Their theory deals only with incompressible flow, so I'm not sure how much this would help aerodynamic simulations, but it's probably got lots of applications in hydrodynamics and industrial process simulation.
You can see the original papers at http://web.mit.edu/ghaller/www/papers.html.
It may be extensible, though
That said, it's totally true that you could use this sort of code in gasdynamics situations where the compressibility doesn't matter much, as you pointed out.
The experimental setup they validated their code with used three liquids -- Fluorinert, glycerol, and vegetable oil -- shearing past each other and the walls of a container while being stirred slowly. All incompressible, true, but perhaps chosen for experimental convenience rather than any problem with their theory's handling of compressibility.
The very fact that they've subtitled their magazine (" Technology Review") as "The Authority on the Future of Technology" is proof of that.
Hell, the fact that they've gone beyond press releases to printing up their own hagiographic magazine is proof of that.
I don't say this to be bitter - as someone for whom marketing does not come easy, I'm perpetually impressed by what a great job they do.