It appears to just be a camera withthat they are using a fish eyemoving lens that maybe does some optical correction internally to rectify the distortion caused. (And is probably only wide in one axis.) Basically, it captures light coming in from a wide set of angles (thus the extreme curvatureexposes part of the lens) and bends it to resolve on the film. There is almost certainly one or more additional corrective elements at any given moment.
I'm not sure if there are any digital camera equivalents, though I'm not sure that you wouldn't get better quality results by taking multiple photos and stitching them together. This is what most photographers I know do and since it is easy digitally, it really reduces the demand for such hardware, so it's probably pretty unlikely unless someone made a lens for a typical SLR to do it.
Update, some quick Googling confirms there are actually digital panoramic cameras available even though I've never seen one in use. They however appear to be extremely expensive specialized devices such as the Seitz-D3.