It's the flexible material that does the trick. Originally, it fits in easily. Rearranged, it fits only with a lot of sqeezing. If you try to do the same puzzle with cardboard or a sheet of paper, you'll see that in the version with the gap the upper rim of the L-shaped section overlaps with the lower rim of the shape above it.
The overlapping area that gets cheated away by squeezing equals the area of the empty square.