Instead of working to develop supercomputers (in the process creating the semiconductor, as was the case in our universe), humanity invested its technological efforts in further harnessing the atom, inventing fusion power. Fusion power allowed the Fallout world a clean, renewable, plentiful and portable source of power.
This meant that things like power armor and energy weapons could be built, as well as all the housekeeping robots. Many such power sources continue to function hundreds of years after their construction.
Computers that fit in a single room!
One of the major divergences is that in the Fallout world, the rapid miniaturization of computers and electronics never occurred.
The transistor was not developed until just before the war, while the semiconducting microprocessor may have never been developed.
As a result, the computers in Fallout are all of the old reel-to-reel tape type and mixed vacuum tube/transistor type and are generally very large and bulky, while displays are small monochromatic cathode ray tubes.
These computers are very advanced in their processing power, indicating that progress continued in this field albeit at a slower rate than in our universe, but the technology to make them smaller never emerged, nor did user-friendly icon-based graphical user interface operating systems.
Consumer television sets and radios also failed to evolve past the early 1960s level.
Physics in a Different World:
The Fallout world does not merely diverge historically. The laws of physics in the Fallout universe are fundamentally different. The “World of Tomorrow” theme is not limited to what technologies exist and how history unfolded; it also applies to the laws of physics, where Science!, not science, is dominant.
In our world, we know that exposure to ionizing radiation merely causes disruptions to cell mitosis (brought on by faulty DNA replication because of the shifting of nucleotides (mainly thymine) by radiation particles), causing cancer and death. In the Fallout world, however, severe radiation isn’t always fatal, and it occasionally produces unlikely or impossible mutations including increased size and, in the case of ghouls, extremely long life coupled with a decaying body.
Classic movies like Them or The Fifty Foot Woman, in which freak nuclear accidents caused giant ants or people to appear, are good examples of the Fallout universe’s take on scientific principles.
All science behaves the way it was popularly portrayed in 1950s pop fiction. For instance, in the Fallout universe, slight irradiation functions like a preservative to keep pre-war foodstuffs edible and unspoiled for hundreds of years. A new beverage product, Nuka-Cola Quantum, deliberately contains a Strontium isotope for lift and kick (and to create an appealing lavender glow!).
Finally, functional compact directed energy weapons exist, with a nod to Nikola Tesla’s research, and such are capable of burning targets to a pile of ash. Robots are capable of hovering about using tiny jet thrusters that never run out of fuel, presumably due to some sort of internal fuel generating system powered by fusion cells.