Thanks for posting, I really enjoy these "first cracks" at mainstream technology. And to think they had this as a working prototype almost 35 years ago (albeit via dead reckoning and not satellite as ashleyn pointed out).
The system just needs to know it's start location (the car factory) and can correct any errors in dead reckoning using the compass and maps.
GPS is so cheap now that there is no reason not to use it, but a system built with dead reckoning today would work just fine.
With dead reckoning the error accumulates over time. Because GPS provides absolute positioning it does not have that problem.
A simple Particle Filter conditioned on "90% chance the car is on a road or other drivable space" will robustly get rid of any error accumulation, leaving you a position estimate that may even typically be more accurate than GPS.