Physics and engineering are not the author's speciality, are they?
It isn't a compass. It's a new method for implementing the venerable concept of an inertial guidance system, which is itself simply a technological form of dead reckoning practised since the first manned boat got lost in poor visibility 11,174 years ago.
Inertial navigation systems are still very important to submarines (such as boomers, spending long periods under water and unable to receive GPS) and I might guess that they would be the first operational priority for this new tech, given that its early-version mass and size won't be prohibitve in a sub, compared with a missile or an aircraft.
It will be extremely interesting to see how the noise problem will be managed. With mechanical weaknesses such as friction removed (it is a core problem of current INS tech), the sensitivity of the new system is both advantage and disadvantage. There will need to be some clever design in dealing with local mascons, determining honest-vs-deceitful frames of reference, multi-axis rotation and relativistic effects—the latter cease to be ignorable when you're finely analysing the performance of kit which may accelerate at 100g, moving in three spatial dimensions, potentially rotating around one or all of those as well, and reaching speeds in the miles per second range¹.
It'll be even more interesting to see what kinds of countermeasures might work against such a system. I'm guessing local EMP would banjax it thoroughly, as would an x-ray laser, not to mention finely tuned peppering by minute chunks of high-velocity debris (strikes by waves of microgram particles timed to arrive in a sequence to ensure destructive interference). That said, if you can shoot close enough to achieve that, you're probably close enough for a kinetic kill anyway ...
¹ Consider that even the 1960s Sprint ABM had incredible performance at this level, and furthermore that a rapidly spinning missile is one obvious countermeasure against laser strikes.)