I wouldn't let him fit a new gear shifter, cable and housing on any of my bikes. The way he cut the housing and the cable, were amateurish. As was pointed out, a cable cutter would have been better. Why would you attempt the job if you don't have the right tools? A cable cutter isn't expensive, and you don't have to mess around with a sharp knife.
When I replace cable housing, I thread it through the frame mountings, run it down to the barrel adjuster, mark it and cut it. This tends to slightly burr the end of the metal part of the housing. I just touch it against a grinding wheel to remove the burr.
I put ferrule end caps on each end of the housing. They help to keep dirt out of the housing. He didn't use any. Then I thread the cable through it.
I don't know what that grey thing is next to the handlebar grip but it needs to go somewhere else. I think the shifter lever needs to be close to the grip. In his case you've got to take your hand off the handlebar to shift gears. And I favor under the handlebar shifters.
The video was poorly done, and he butchered the job.
Here's a view of one of the shifters on my fat bike. Notice it's under the handlebar and not over it. I also have a hybrid bike that came with twist shifters. I changed them for lever shifters, again, under the handlebar. I can just touch them without taking my hands of the bars. If you're going to buy new shifters, you need to consider which types are best to suit you. And don't forget they have to match the derailleur; don't use Shimano shifters if you have a Sram derailleur. It might work if you're lucky but it's best to match them.