You are correct, it is not based on SQUID. But, I think SQUID is technically a class of quantum magnetometer? Quantum magnetometry is pretty vague, since most high-end magnetometers use some sort of quantum mechanics.

I think the term you're looking for is atomic-optical magnetometer. Someone posted a DARPA project (AMBIIENT), that uses one. What's special about the atomic-optical magnetometer, is that it measures the gradient directly. With SQUID, if you have two SQUIDs in a uniform magnetic field, you can't determine the vector of the field. But, with atomic-optical magnetometry you can.