I hope this is the same knot:
a girth hitch, plus a tucking, form a big hole, then push a bight into that hole, done.
You describe it as it it was easier than it really is...

Tucking through
which of the many possible "holes" of the Girth hitch ? After this tucking, the working end goes "over" the two eye legs - it could well go "under" them. And the last bight, that penetrates the main coil "tube", penetrates the (red, highlighted) bight formed by the returning eye leg, too - it could well go "over" or "under" it.
It is
almost the same knot - the minor difference would probably make
almost no difference, and would probably be noticed by
almost nobody

. I had a concrete reason I tied the knot as shown in the original presentation, and not in your variation ( which I had also considered ). Just follow the standing part : You will see that its first curve, which is the most important squeezing/securing segment of any eyeknot (because it carries the 100% of the load ), in your variation comes in direct contact mainly with the last segment of the tail, which is free-floating ( In fact, the only reasons this loosely connected last part of the tail ( the tail of the tail...

) goes through the coil "tube", is to enhance the stiffness of this pseudo-Zeppelin s loop "pivot", and to widen the diameter of the standing part s first curve ). In my variation, the first curve comes in contact mainly with the functional ( regarding slippage ) part of the tail, the segment before this last tail-of-the-tail one. It makes no sense to "waste" some of the nipping power of the standing part s first curve just to secure even more a segment that is not tightly connected to the rest of the line... So, in my variation, I twisted the "pivot" bight as I had, in order to concentrate the nipping power of the first curve on the functional ( regarding slippage ) part of the tail, not on the tail of the tail.