I hate to be the negative guy, but isn't this the obvious, standard, well known way of building a greenhouse? You want to prevent hot air from escaping, you put up something that contains the air. An actual greenhouse doesn't really rely on "the greenhouse effect" of allowing visual light to pass but being opaque to infrared. It's all about preventing hot air from rising. This can be easily seen in polyethylene windowed greenhouses, which get just as hot as glass greenhouses, even though polyethylene is just as transparent to IR as to visible light.
That part of the piece seemed like something the MIT press office coaxed out of them to get a human interest angle TBH.
Really, most of their improvement over the 2014 version seems to come from the spectrally-selective absorber coating, which is a lot more expensive than bubble wrap. So they say this solution might be ~10x cheaper than existing solar destilling plants, but they also say it will need replacement ~10x as often. So depending on exactly how the numbers work out, this might mean slightly cheaper, more labor-intensive desalinisation plants, but we're not covering any deserts just yet.