It is even less decisive than you're saying.
The fact that the Supreme Court decided not to overturn the decision of the Court of Appeals for the Federal Circuit that APIs are copyrightable means that binding precedent on every court except the Supreme is that they are. And for fair use, one of the statutory factors is the "effect" of the copying on the "market for or value of the copyrighted work."
That said, this case does establish a precedent that if your copying of an API is primarily for purposes of matching an interface so that developers can reimplement it, you're in fair use territory:
The fact that one statutory factor points one way doesn't stop another from pointing the other. And part of their decision is the conclusion that Google's copying increased the value of Java. That will generally not be true when APIs get copied.
In particular if I am trying to create a product that competes with yours, and I copy your API for the purpose of interoperability, I'm going to have an uphill battle claiming fair use. Because my product directly reduces the market for your product.
To name some historically important examples, Microsoft copied the APIs for JavaScript from Netscape, Microsoft copied APIs from Lotus 1-2-3 for Excel, and Wine copied APIs from Windows for Linux. The outcomes famously were that Netscape went out of business, Lotus 1-2-3 was discontinued, and Linux became somewhat more viable.