It is unclear what was wrong with the first repair. The video you referenced is from the Tire Industry Association - a US based tire organization for tire dealers primarily known for its training programs. This video appears to be for that training purpose and I think you can consider it authoritative.
However, the video not only shows the right way to do a tire repair - as well as several examples of improper repairs - and it is not clear which you are pointing to.
However, I am sure you can figure out from the video what is a proper repair and what is not.