The parent's point is that it cannot increase the transmissivity of the material it's mounted to even if it is highly transmissive, thus in combination the composite will not be more transparent/transmissive than glass.
It will obviously deliver more total light if the structutred surface gathers more light than the flat surface.
If that's what's going on then it's no more mysterious than the difference between a cloudy day and a sunny day shining through the same pane of plain glass. When there is more light on one side, there is more light on the other side.
And that does seem to be the mechanism actually. Other commenters have pointed out this article just isn't very good and the original source never says transparent and does descibe explicitly that the surface is simply gathering more light by allowing less of it to reflect away. Light that would have reflected away is instead redirected inwards.
"Gathering more light" is generally proportional to its planar surface. In the case of a surface film the potential increase in projected planar area is minuscule.
If you imagine an incident ray, to have a material "gather more light", that ray needs to intersect the material whereas without that material it would miss the surface. By adding some amount of height the film may cause some rays to intersect the surface that wouldn't have (primarily around the edges) but that's going to be very very small.
In general its a safe assumption that any material of the same projected planar area you put in front of another material will reduce the total transmisivity of the system.
