I don't have a video, but I can give you an idea of how I would do it, based on what I know of the gigaminx.
Start with one face and place 2 adjacent main edges in + their centers (star points). Then place the rest of the centers between those two edges, then the corner and edges, and top it off with a main edge + star point centers. You should have 1 corner assembled now.
Continue with the bottom face until it is entirely assembled.
Above each of those main edges that you topped the bottom face off with, assemble the corner, using the same method as before.
Continue until you have all of the corners touching the bottom face corners assembled.
Then assemble the corners adjacent to those until you only have only the top face corners left.
This is where it starts to get a bit more difficult. My suggestion would be to take off the top center cap and unscrew it almost all the way, but you still want it to be in, just very loose.
Pop all the main edges and corners in, as those are the big pieces that can't be put in later. Then put all of the centers in, starting with the bottom ones, then the top ones. Lastly pop in all of the edges.
Tighten the top center again and put the cap on, and bam, it's assembled.
If you need any more elaboration just ask
Also if someone who actually has a teraminx can confirm this, that would be nice, but I don't see why the instructions would be wrong.