Because the re-arrangement is a cheat.
In the center is a rectangle, 1 x 3 ( h x w ). Find this in the original figure and you notice that the diagonal does NOT cross from corner to corner but misses it just ‘smidge’ at both corners. In the re-arrangement, this is ‘corrected’, although the result means that this line, when extended to the ‘new’ corners, actually ‘bends’ slightly as it passes through the indicated rectangle.
Don’t see it ? Try expanding the image and laying a straight edge along this diagonal. Otherwise, get some graph paper and actually cut out the figures and lay them out manually.
BTW: This is derived from centuries of obsession with the so-called Fibonacci Series ( 1, 1, 2, 3, 5, 8, 13, 21, etc. ). The chosen dimensions occur in consecutive elements of the Series. You can construct similar ‘paradoxical dissections’ with dimensions 2, 3, 5 or 13, 21, 34 or whatever.
YMMV
21stCenturion