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.