Does microwave radiation have any effects beside heating?
Yes. Take a look at this study.
Comparisons were drawn between irradiated samples and samples exposed to elevated temperatures within a furnace to extract microwave specific heating effects. The microwave-heating environment was found to exhibit unique effects
Is the effect unique to microwaves?
The Atlantic article in the question provides references to support its claims:
And a group of researchers led by a Berkeley Ph.D. student presented technology at a 2014 conference that could “hear” what people were saying by analyzing the distortions and reflections in Wi-Fi signals created by their moving mouths. The system could determine which words ...