“They were using slide rules. They did not have computers on board. It was amazing. And they could have died a thousand different ways. It was truly amazing.”
They did have computers, but primitive as hell, and it took super-human skills to squeeze the code to fit the tiny memory.
Yes. Their computers were extremely rudimentary but mostly worked.
Remember, when the Eagle was landing Armstrong and Aldrin kept calling out a certain number over and over. It was the computer buffer overload code so Armstrong took over and manually flew the Eagle to touchdown. Because of the terrain they had only a few seconds of fuel left to burn at touchdown and that is why Mission Control said they had a lot of people breathing again.