From what I recall when I skimmed the original paper, you would need more general hardware than the wifi chipset in a phone. Actually, that this says it uses wifi at all is a bit misleading. It happens to work on the same frequency bands that wifi uses, but their experiments did not actually use wifi hardware at all and actually used USRPs. Getting off the shelf wifi hardware to do the same would require firmware and drivers that allow raw access to the radio signals, which no cards I know of come even close to.
Additionally for their experiments they needed at least five antenna, so even if it were going to happen with phones you'd probably need more than just two.
Actually, this is similar work but by different people. The links you posted are about work at University of Washington, whereas the OP is work done at MIT.
https://news.ycombinator.com/item?id=5824286
https://news.ycombinator.com/item?id=4334264
I'm still waiting for someone to make an app that does this -- would it require linking 2 phones?