Aside from the fact that peppers don't grow from the stem like that (notice the location of the blossom in the earlier shot), and there is no sign of roots on those potatoes, I have some questions.
Five days for pepper germination?
Why the constant use of rooting hormone? Is that supposed to be fertilizer?
What is with the egg?
That baby pepper is way too small for grafting. I want much more detail on the grafting process. What I see doesn't make sense.
Garlic??!! What are the garlic and aloe vera for? He feeds it separately...
The dirt would not stay in the bucket, no matter how perfect the fit.
While it is possible to graft a potato and a pepper, the potatoes in the final shot are not attached to any kind of root system. The peppers are also not attached. The soil would be far more compacted. The potatoes would be deformed from growing so close together. And while it is possible to get that many potatoes from one plant it's highly unlikely.
My conclusion: while this may be a possibility, this video is a fraud. I would need far more information on their process to determine whether it would work as shown.