They begin their video by acknowledging that the Fallout universe is in an alternate reality, but they provide an incorrect general explanation. The backstory is that the world was caught up in the Resource Wars. It is better to read the Fandom Wiki which best explains the situation behind the resource crisis.
The Resource Wars is an umbrella term referring to over 25 years of conflicts from the war between the European Commonwealth and the Middle East in April 2052 to the Sino-American War and the Great War on October 23, 2077. Some of the conflicts included the annexation of Canada by the United...
fallout.fandom.com
In conclusion:
The last war, known as the Great War, in the Resource Wars, was instigated by corporations. Nuclear energy became imperative when petroleum reserves started to dwindle. There are other themes involved, but too much to discuss.
This explains it in short:
Technology appears in several variants throughout the Fallout series. Technology in the world of Fallout is different from ours, due to the Divergence. Much of Fallout's setting is inspired by 1950s pulp science fiction. The world is not our own, functioning due to a different set of rules. It...
fallout.fandom.com
The above is explained in the Fallout Bible, which is not accepted as lore anymore, but the above is how it is known in the universe. The wars are all acknowledged in-game, as is the resource crisis. Bethesda even tied Fallout 4's, The Sole Survivor, to the Sino-American War /cough. I guess he did some time in cryo
The world, or rather the US, is stuck in the "50s" because they isolated themselves, and in the process to counter their collapsing economy put their resources into advancing technology. I am sure it will all be explained in time on the TV show. As known, Vault-Tec ensured total nuclear war.
There is way more to their Ghoul explainer. Here is VATS illustrated, with caveats, having unlimited action points: