Yes, it is absolutely a real Unix system, it was a Silicon Graphics workstation (using IRIX, the SGI System V based Unix) running the three dimensional file system browser fsn ("File System Navigator", pronounced "fusion").
Silicon Graphics were early developers of hardware acceleration for 3D graphics, so it made sense to themthey had the capability to releasecreate a 3D file system viewer in 1992, a year before Jurassic Park released.
The fact that the SGI logo is visible on the monitor, makes me wonder whether this was an example of product placement.
References: Wikipedia:Silicon Graphics, Wikipedia:fsn, SGI-Stuff