It had a stylus that contained laser interferometers that could very accurately and precisely measure the distance from the stylus to the grove walls. It kept the stylus near, but not touching, the groove, getting the audio signals from the variations in the distance to the groove.
In addition to not causing any wear, I remember reading an article back then in one of the audiophile magazines that said it also made records that had already been played many times on regular turntables and were degraded sound new, because the Finial could use a part of the groove farther down than had been used by the regular stylus, and so was not worn.
It was going to be pretty expensive, around $8000 at today's prices, so was probably only going to be affordable to radio stations, archivists, and high end audiophiles. Then they got hit with the double whammy of a major recession and the rapid replacement of a large chunk of the vinyl market by CDs.
Finial was liquidated in 1989, and their patents ended up at a Japanese company. Development continued in Japan, and eventually resulted in a product [1]. They seem to be around $15000.
The Library of Congress and a couple of other places have a system that can recover the sound for vinyl records and old wax cylinders what works by photographing the grove through a confocal microscope. The thousands of photographs are then analyzed to figure out the audio signal. This is still research level stuff, I believe, not aimed toward producing a commercial product, and so would be even farther out of reach for consumers than the laser interferometer turntables are.