He had to cut milling bits with custom profiles to cut custom tools such as a series of graphite and copper spark eroder forms to cut just some of the corners and shapes in the (paper) technical drawings, then repeat for the next ill-advised bevel or interior sharp angle or even lettering which is too close together to get a milling bit inbetween two letters. Figuring that out was his responsibility alone. Instead of computer control, he'd have to do something like first create a scale model of part of the tool out of a block of plastic, then use a pantograph (a mechanical linkage allowing you to trace a shape with a pen and have the movement magnified/minified) to copy the shapes on a milling machine -- even shapes that seem simple. And then maybe throw away (actually, take home as a souvenir) a month or two's work if you cut slightly too deep -- these were high precision parts. Not because the plastic had to be so precise, but because the completed dies are made out of many steel parts that have to fit tightly together and slide past each other, as you can see in the article.
Considering the ~two months quoted in the article for this mold, I'd think a lot of that complexity is still essential despite modern computerized machining. I'm sure a great deal of ingenuity and many steps are still needed.