You may have missed the final phrase in the video repeating twice: "one hundred percent"
So first, how is it magically 13% remaining power becomes 100% new power.
Second, assuming first question answered, it is 100% for shit sake, not 800%. False advertising!
100% / 13% ~= 8x
It's a completely misleading "test" though. The battery level indicator uses the battery voltage to estimate the remaining capacity. As soon as you introduce a device to modify the voltage being measured, the indicated battery level becomes absolutely meaningless. Sure it reads 100%, and it will continue to read 100% until it suddenly and inexplicably dies (probably around the same time that it would have died anyway...). The batteriser will do a GREAT job of rendering the battery level indicator on every single device it's installed in completely useless.
A REAL test would be to put brand new batteries in a keyboard, run some kind of benchmarking test until the keyboard dies, and measure how long it took. Then restart it - take new batteries, put them in a batteriser, run the same benchmarking test until the keyboard dies, and compare the run time to the first test. Then repeat each of those tests a handful of times to get a nice average. If the runtime with the batteriser is 8x longer than without, I'll eat my words, but it won't be. I wouldn't be surprised at all if it even hurts the run time due to switching losses, since I assume the Apple keyboard already has a DC/DC converter inside that's designed to extract a significant amount of the battery capacity, in which case adding the batteriser just doubles the switching losses and runs the battery out faster. I suspect this will be the case with most other consumer devices as well.
I also suspect that they KNOW this, and the fact that they haven't provided ANY measurements for ANY devices shows that they have nothing good to report, and they're bringing it to market anyway. The fact that they have to resort to false advertising (battery level indicator showing 100% on a depleted battery) is VERY telling of the lack of confidence they have in their product. If they had something real, they would show it, instead of resorting to deception.