The article begins with an example of what the author seems to think is truly outmoded technology, only useful for teaching preschoolers. But people who know how to use the abacus can multiply a couple of four-digit numbers together, arriving at the result before an experienced electronic calculator user has finished entering the first number into the machine. I've seen shopkeepers in New York's Chinatown using abacuses in place of cash registers, and I'm sure their use is still widespread in China, at least. Electronic calculators begin to have an edge when you need to extract square roots of numbers more than a few digits long.
There is a pattern here: old technology often requires some training to use it effectively, but if you put in the work to develop the skill, it works better in some situations.