Nothing mysterious nor does it appear to violate any physical laws. It simply relies on radiation pressure. The description is somewhat misleading regarding “no tradition fuels”, but generating microwaves obviously takes energy, usually electrical to drive klystron or magnetron tubes. So think of a wave guide (pringles can) attached to a nuclear battery. The poynting vector goes out the tube nozzle producing radiation pressure, and by conservation of linear momentum our battery and wave guide go the other way.
I think you have it right.
The microwave source requires a sustained energy source that will slowly but surely be consumed. If so, you are right that there are no fundamental laws in jeopardy here. But there may be some NASA calculations that are.