The theories from before WWII of Walter Schottky were indeed an important step in the development of semiconductor physics.

Besides Schottky there are a great number of other people who had critical contributions towards the development of semiconductor devices and who are not mentioned in the very short summary from the video.

For instance, Julius Edgar Lilienfeld had invented before WWII 2 kinds of field-effect transistors: metal-semiconductor FETs and depletion-mode MOSFETs. But before WWII making such devices was not reproducible, because the available semiconductor materials were too impure.

Nevertheless, the Bell team searching for methods to make semiconductor triodes was aware of these patents and they were stimulated by them to find alternative structures that worked.

The work of the team that discovered the point-contact transistor would have been completely impossible without the techniques developed during the war by some of their colleagues, e.g. by Russell Shoemaker Ohl, for making pure germanium and silicon and diodes using these materials. (During the war, Ohl has also invented the silicon solar cell, as a byproduct of the work on radar diodes.)