It's somewhat unlikely (but not impossible) that this method is based on navigating by matching patterns of the shape of the geoid (aka variations in g).
We need accurate maps of the geoid for a lot of different reasons. (Military as well as civilian. Potential fields geophysics is super useful for all kinds of different geologic use cases, and regardless, if you want to target an ICBM, you need an accurate geoid.)
However, a super precise gravimeter doesn't help much. We have more precision than we can use already. Rather ancient spring-based instruments from 100 years ago can actually still give more precision than we can use in many cases. Modern ship-borne gravity instruments work on different principles, but the signal is very noisy for the same external reasons.
The biggest issue is that you also need to know absolute elevation very precisely to use the measurement of g that you get. A few millimeters of error in elevation significantly changes the anomaly measurement you make. Sure, submarines can get accurate hydrostatic measurements of depth, but those assume a lot of things and critically aren't absolute. The ocean has currents - that's another way of saying that the surface of the ocean isn't "sea level". Those vary through time and would require satellite information to correct for. However, once you get down in the weeds, it gets tougher still.
Remember that we're dealing with an inverse square distance relationship. Things close by matter quite a lot.
People nearby standing in different positions? That actually does affect things. Easy enough to mount the instrument away from people, though. Different distributions of mass in the submarine? Also affects the measurement. You can correct for all of these in various ways, though, so long as you have information on it. It's just more complexity and another source of noise.
In the end, the "free air anomaly" measurement you'd be correcting things to is an bathymetry map, to the first order. If there's a landslide, that affects things quite a bit, and those happen all the time.
Finally, you'd be matching a "fingerprint" time series measurement as you travel to a pre made map. That's a non unique relationship. You'd have heading/etc information to help the non uniqueness part significantly, but when things don't vary much (i.e flat topography and not a ton varying geologically), you don't have much of a unique signal to match to.
At any rate, it's a very useful tool for many other things, but I'm skeptical it could be turned into a precise navigational aid. In combination with traditional gyroscopic/etc measurements of heading and distance, it could help constrain uncertainty, but it's not an independent measurement and it's relatively noisy.
Now that I think about it, though, a fully passive "seamount proximity sensor" is rather useful, and that's something you'd get even with a noisy signal...