I agree. The author laughably claims APIs are how applications take to each other and implies they are necessarily remote or on the Internet. Web APIs are one kind of API, but so are various C Library interfaces.
It is an ad. It worked. Don't expect a car advertisement to teach you how an engine actually works.
Don't expect a car advertisement to teach you how an engine actually works.
Why not? [1]
The idea that APIs are a singular thing - or started as late as the article suggested - is also sufficiently wrong to put everything else written in the article into doubt.