I did read the post but you are guessing as you don't know if the lenses are not thicker.
Knowing is better than guessing.
Canon have not said how they have reduced the weight. If it is by reducing the size of the elements I would prefer them to tell me rather than become involved in speculation.
The elements would have to be a lot thicker not to be lighter if their diameter has been reduced by so much like it has.
Some rough maths, both models have the same dimensions, 163mm x 343mm. If that drawing is to scale (and it seems like it could be due to the width and length ratio being roughly correct for the stated lens dimensions) the drawings is a 1:4.075 ratio. Going by the drawing the older II version the element diameters are roughly 120mm, 100mm and 80mm and the elements roughly 8-12mm, where as the newer III version element groups are roughly 84mm, 80mm and 76mm and look to be the same kind of thickness 8-12mm.
The element group areas would roughly be:
II Version:
120mm element, area = 11304mm2
100mm element, area = 7850mm2
80mm element, area = 5024mm2
total area = 24178mm2
III Version:
84mm element, area = 5539mm2
80mm element, area = 5024mm2
76mm element, area = 4534mm2
total area = 15097mm2
If they aren't a similar thickness, the newer III lens elements would all have to 1.6 times thicker than the older II version elements to have the same volume and therefore weight (working on the idea that the glass elements weight density is similar and hasn't changed in any way).
Canon have said how they have done it but not gone into specific details such as dimensions and thickness of elements, other than say they moved the element group backwards therefore reducing it's diameter because 1/ it's way above most peoples heads 2/ it doesn't really matter and 3/ its their sensitive commercial information.. Canon are never going to go into a large amount of specific details as that kind of information is likely to be quite commercially sensitive and you don't tell your competitors your secrets.
We have to take what they have said as the most info we are going to get.
In the video linked above:
@0:45 weight reduction due to optical redesign, barrel redesign and IS improvements.
@1:22 front fluorite elements moved back into the middle of the lens, A BIG REASON FOR THE WEIGHT REDUCTION.
Add that to the 'revised optical design for a lighter weight super telephoto EF L lens' info posted by
@jakeblu its clear to me how they have done it.