In loose terms: It does this with a special read head that splits one of the recorded tracks into 2 distinct signals (for a total of 3 signals from 1 stereo recording). The split tracks' signals are compared, and it adjusts the azimuth (by minutely rotating the head) until the signals from the split track match most-perfectly.
A better overview is found in this sales flyer: https://www.richardhess.com/manuals/Nakamichi/dragon_folder....
(Take note of the pictures of the machine. If anyone finds one sitting around at a flea market or in a forgotten pile of old junk, please rescue it. Nothing like this will ever be manufactured again. Even if the condition is "it looks like someone went after it with a big hammer as part of their anger management process," the bits that remain still have significant value and are easy to sell.)