The video clip is short, but there are mistakes, further procedures that should be done, and some things he did that should have been done better.

Three particular points:

He stated in reference to the debris screens in the washer hoses, "on the machine side of the hoses." The screens shown are typically at the faucet side of the hoses, not the machine side. There are screens at the washer side (which do need to be cleaned), but they are inside the water valve connections, not in the hoses.

The reference to running a maintenance wash to clean out accumulated debris and oils is correct ... but since the scum collects at and slightly above the normal level of the water, a gallon or so MORE hot water needs to be added to raise the water level above that scum line for the maintenance wash. Full and proper cleaning of a long-neglected washer may require disassembly.

When he pushed the dryer back into position, the flex duct should have been aligned (if at all possible) to collapse onto itself for a straight shot between the dryer and wall, instead of formed into an S-curve as was shown. Curves and bends can cause restriction on the airflow resulting in longer drying times and even overheating and premature failure of an electric heating element and the machine's safety thermal fuse (both gas and electric).

By the way, the "old" ducting that was removed ... that was likely a prop for the video. It was kinked so badly there's no way the dryer would have worked.

Dadoes is correct, there was a lot of mistakes made!
In general, washing machine MFG hoses comes without the washer screen that was shown, so the problems will lie at the washer valve screens on the back of the machine. Those screens can be brought at any plumbing store for $2-3.00 for extra protection to the washer machine valves. It's easier to clean the one connected to the incoming than the one on the back if the machine.
Also, when he put the washer back, the washer needed to be releveled.

As for the dryer, he replaced with the wrong aluminum flex hose. The same semi ridged ducting could have been replaced and cut to reduce length. Since that duct was right there, a ridged piping could have been used straight from the dryer through the wall or if there is space in the room where the dryer duct can be move to the left or right of the machine, then it can be exhausted that way without the dryer sticking 7-10 inches away from the wall.