The underlying technique of the light stage is to record a zillion photographs of a real subject being lit from a zillion different angles. 1 light per photograph. Then, to show the subject being lit in a new environment, you convert the lighting environment to a (conceptual, not literal) cube map and modulate each of the lighting photos by 1 pixel of the cube map. Add all of those modulated lights together and you get a newly lit image of the subject. At that point it is "just" a matter of compressing the hell out of the lighting photos and smartly streaming and processing them fast enough to preview it in real time.
Advantages:
*The result looks perfectly real (to the limit of source image resolution) because it is basically a photograph of a real person.
Disadvantages:
*The data set is huge -even after compression. The video mentions 21,000 images.
*The subject is static (Unless you can handle enough images to make a movie. Then you can have a pre-recorded video like the brunette OTOY showed off a while back.) Also, the camera is static. Basically, all that you can change is the lighting.
*No local lighting.
*No mesh to work with. Just photographs.
Now, OTOY is a bunch of smart guys and they have a lot of tech that I don't know much about. They might have some crazy GPU voxel raytracer that can animate the light stage data and make everything awesome. But so far, this is the best of my knowledge as to how it works.
EDIT:
Looking at the video again, they do rotate the view around 1 axis. I suspect this is similar to the QuickTimeVR trick of scrolling through a movie of the camera rotating around the subject.
Still... it's a neat technique and it's great for film, but I won't get excited until I see it being used on an arbitrarily animating model.
With a real full 3D mesh or voxel dataset you'd have a completely free camera.