Section 2.1 in their linked paper (
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/201...) gives some clues. I think this is what's going on:
GPS receivers work by figuring out how far away they are from a number (>3) of GPS satellites. The receiver knows where the GPS satellites are (since the satellites broadcast their orbit parameters) so if a receiver knows how far it is from several satellites it can work out where it is itself.
Now, as the GPS satellite signals travel through Earth's atmosphere, they can be slowed down by different atmospheric effects. A slower signal will cause the receiver to think it's farther away from a satellite than it really is, so the receiver might estimate that it's position has changed a little bit. However, if you know the receiver's position hasn't change (maybe it's fixed in place to a big rock), then you can attribute the receiver's measured "change in position" to a change in atmosphere characteristics.
In this paper, they seem to have lots of fixed GPS receivers all over the place. By looking at all of them together, they can make a sort of map of the atmosphere characters in a part of the sky that's affected by rocket launches. The authors see these big ripples emanating from a Falcon Heavy launch in the US and this tweet shows those same ripples emanating from a launch site in North Korea.