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I think there may be some older files mistakenly uploaded, because I downloaded this all in one shot (zip archive) and the files don't match the instructions, and the operation depicted in the video is physically impossible.
For starters, the small ring is supposed to be able to rotate within the larger ring, but it can't. The holes where the drive shaft goes from the flat outside gears to the cube gears are round, so rotation is possible on that axis, no problem. However, the holes on the opposite side are BOTH semirectangular. The pin cannot allow rotation between the large and small rings because the flat sides of the semirectangle lock both rings relative to one another, making it physically impossible for the small ring to rotate relative to the large one. This is a showstopper.
There is also at least one pin that's too short. cube_pin_fixed passes from the cube gears through the small ring, but stops only part of the way through the large ring, so it can't engage the largest of the three gears. I verified that it's the longest pin supplied in the "thing files," which it is, by far. I elongated it by 8mm and it seems to work fine.
"The œcube_pin_fixed then goes through the hole in the small ring and locks into the hole in the large ring. Make sure that the small ring turns smoothly around the pin."
OK, so far, so good...
"Next insert the 8x20 pin through the hole on the other end of the large ring and lock it into the small ring."
The large ring has two inside holes, one of which is occupied, so you must mean the free one. A 20mm pin will not fit there. I think you meant one of the 13mm pins.
"You should be able to tun this pin while holding the large ring and have the small ring and cube gears turn."
That pin is supposed to allow rotation, but its sockets in both rings have a semirectangular profile, which makes rotation impossible without destroying the pin. It would only sieze up and grind gears if you tried to turn it through by hand. In other words, the device cannot function with the supplied large and small ring STLs.
Also, it looks like the site has corrupted the instructions. There's garbage characters and no spacing between paragraphs. It did this to me a couple years ago as well. If you reformat the instructions, they should stay legible from now on.