The picture at the top on the right is an etching by Escher. Lipson and Shiu computed what the distortion was on the image, then undistorted the image to create a "clean" picture of a village. They then built the village in Lego, photographed it, and applied the computed distortion to that photograph to create the image at the top left.
The pictures throughout the rest of the post document what they did, and what the model looked like from other angles. You may think it's implausible, but I can assure you that it's all true, and that's why it's impressive.
As to the use of "rendering" I'm assuming you mean this:
> I wondered for some time whether it would be possible to produce a plausible rendering of any of his pictures in LEGO bricks.
Basically that's just asking if they can produce a duplicate of the Escher image by photographing a Lego model and applying a distortion.
Which they did.