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 from a list of lip-readable vocabulary were being said with 91 percent accuracy when one person was speaking, and 74 percent accuracy when three people were speaking at the same time.
That link points to the details of a 2016 article, We Can Hear You with Wi-Fi! (available here as a PDF) which describes the prototype project consistently with the Atlantic article:
This paper presents WiHear, a novel system that enables
Wi-Fi signals to hear talks. WiHear is compatible with existing
Wi-Fi standards and can be extended easily to commercial
Wi-Fi products. To achieve lip reading, WiHear
introduces a novel system for sensing and recognizing micromotions
(e.g. mouth movements). WiHear consists of two
key components, mouth motion profile for extracting features,
and learning-based signal analysis for lip reading. Further,
Mouth motion profile is the first effort that leverage
partial multipath effects to get the whole mouth motions’
impacts on radio. Extensive experiments demonstrate that
WiHear can achieve recognition accuracy of 91% for single
user speaking no more than 6 words and up to 74% for hearing
no more than 3 users simultaneously.