The D4 is still a 14-bit RAW camera according to Nikon's own specifications page:
NEF (RAW): 12 or 14 bit, lossless compressed, compressed or
So, it cannot capture 16-bit images off the sensor, at best they are still 14-bit. If I understand the page you linked, it sounds like they are saying the Expeed image processor chips are fully 16-bit. I don't know that there is really any benefit there...that would be like saying 24-bit RGB images are processed using 32-bit numbers on a computer. If there is any floating-point processing involved, then the additional bits mean more precision, however I can't speak to that, as I don't know what kind of algorithms are used (I would assume integer algorithms are faster...) The 16-bits is just the word-size of the camera's CPU, for all intents and purposes.