You are correct. As of this time California is not requiring smog inspections on diesel cars 1997 and older, so you should not need a smog check when attempting to register this diesel 1983 VW Rabbit.
We recommend contacting the Bureau of Automotive Repairs at (800) 952-5210 prior to purchasing this diesel VW in order to ensure regulations have not changed. We are currently undergoing major smog inspection law changes in California. The BAR reserves the right to implement into the smog check program any vehicle it deems necessary for air pollution reduction. Typically notice is given in advance however the public may not learn of new policies until they experience the change themselves.