The author could make the argument that changes in the patentability of one meaning of API could impact the other meaning of API. Instead, while purporting to define the APIs under discussion. they talked about the Twitter sense instead.
They then discuss Java's API in terms of "Open" vs. "Closed," which appears to refer to how easy it is to register for an API key with web APIs. When you are using an APIs of the library kind, the files you are interacting with are under your control--there is no registration, there are no API keys.