Since it doesn't really go into it, what happened was the operators were supposed to manually remove the control rod a few inches to re-attach it to the mechanical mechanism that moves it in normal operation (it was disconnected for shutdown and maintenance of the reactor), instead they removed it like 2 feet. This caused the reactor to go prompt critical and flash boil all the water in a few milliseconds. This steam explosion deformed and launched the reactor vessel and all the hardware on top into the air. The operator that was originally standing over the reactor was impaled (groin to shoulder) to the ceiling with a shield plug. They all died from trauma from the explosion, but the radiation would have done it too.

The (now obvious) change in reactor design that came from this was that no one rod, even when fully removed or stuck in the withdrawn position should cause an unstoppable chain reaction. Although even at this time most reactors didn't have such a flaw, but the SL-1 was designed as a relatively small reactor for remote arctic radar installations and things, not a commercial power generator, which is why it lacked any kind of real containment building or extensive infrastructure- the components needed to be simple and standard, able to be air lifted and minimal construction to put it together.

IT CAME FROM OUTER SPACE

I watched the longer version.

There's just something fascinating about this era. Not only the scientific discoveries, but also the way these old films look and sound. No wonder it's been a plentiful source of ideas for movies, tv and video games.