Technically the shape itself repeats like a mug, infinitely tiling the plane. However, that tiling is not overly repetitive -- if it's like the Penrose tiling, it can be self-similar in a handful of rotations about a single origin, but unlike a square tiling, does not admit infinitely many self-similarities.
You’re right that the shape is used again and again, but the pattern of how it is laid does not repeat. So the new thing here is that there is a single shape that can cover the plane AND that it does this without the pattern repeating (and as an aside it cannot be made to do it with repeats)