How does this compare to the behavior of nonlinear optical crystals like lithium triborate? They are also pumped at a lower frequency (e.g. 1064nm photons) but lase at twice that (532nm).
In some way, it's the inverse: a nonlinear optical system can multiply frequencies, while a time crystal divides a frequency. That's not as easy as multiplying, due to the symmetry concerns I mentioned.
It's basically a frequency divider, but as a system of cold atoms instead of an electronic circuit, and in a different frequency regime.