I found this new video. It uses out-of-production parts like the transmission parts. So when I tried to buy these elements in new Technic sets, I didn't find some of them. Any suggestions please?
There is no universal LEGO Technic set that contain each and every gear LEGO has ever produced.
None1 of those elements are out of production. You may not acquire all of them in a single set, yes, but they are still pretty much available in sets from 2021-2022.
1 Except, maybe, Technic Driving Ring 2L. But it isn't something that cannot be fixed by buying this element from Bricklink or an older LEGO set containing it. You can also modify this creation (it is rather easy) to include 3L version (in combination with Technic, Driving Ring Connector) of the mentioned element which is found in recent sets.
Because the builder had those parts, and knew how to use them.
Perhaps those parts weren't out of production when that was build. There are extremely few MOC's that are updated when the parts go out of prodution. Perhaps the builder doesn't even have anymore, and their interests may have shifted. It does limit how many others are able to build a copy, but that is generally not why people build things.
(Apart from wanting to say that - and it became a little long for a comment - I agree with RSchulz in his answer: because it works.)