An explanation could be provided by irradiation and evaporation of planetary envelopes.
The introduction in the article by Bourrier et al. 2018, which is the source of the NASA press release, explains that as exoplanets migrate inwards, they are increasingly challenged to hang on to their envelopes due to irradiation and heating (insolation) by their star.
The Neptune-sized planets are less capable of retaining their envelopes because of lower densities and lower "surface" gravities. The idea is that many of them get stripped of their outer envelopes and end up as "Cthonian" planets that are of "super-Earth" size.
A hypothesis is that many hot Jupiters have enough mass and density to maintain a large size for billions of years and hence it is only the hot Neptunes that are depleted.
The recent work on GJ 3470b (cited in the NASA press release) supports this hypothesis by finding a very large atmospheric loss rate from a Neptune-sized object at the edge of the "hot Neptune desert".