Does the presence of third party Skyrim mods mean that everything they refer to is an API and therefore non-copyright? The game geometry, maps, characters and events are facts about Skyrim that those mods need to operate. Does this therefore imply that a hypothetical person could sell their own re-implementation of Skyrim on the grounds that all those things (characters, missions, events, geometry, models, etc) were function required for mods to continue to operate?
Or, to stretch it in a different direction, let's suppose I write some functions. If you write some functions that call them, presumably my API is therefore functionality and non-copyright? But what about if you don't call them, and only I happen to write calling code. It's still an API, it's still functionality required for other code to operate (my own), so is it still non-copyright?
What about whether I mark my code public? If I omit "public" from the same function definitions so they can't be called externally do the definitions become artistic and copyright? If so then is the artistry in the lack of a public keyword? If not then is any code structure copyright - it's all functionality that calling functions requires to operate.
Yes, that's deliberately playing logic games and taking things to extremes to see if there's a clear line in the sand. It's going to be interesting to see what the court determines, anyway, because it seems like a big question.
You're supposing that function being uncopyrightable narrows the copyright in the expression, but they're really just two completely different things.
Let's try an even more extreme example. Remember those anti-piracy book codes from a few decades ago? They'd sell a game with a printed manual and then to start the game you'd have to type in the third word of paragraph two on page seven of the manual.
We'll take the game copyright itself out of the equation by saying that the software is cheating by trying to restrict a copyright year 1800 work (expired copyright) using a copyright year 2000 book.
The book itself is clearly subject to copyright. It could be Harry Potter for all that matters. But the third word of paragraph two on page seven? That's a fact about the book. As is the fourth word of paragraph two on page seven, and so on.
If you collect every single fact about the book, you have all the information you need to reproduce a copy of the book. That neither means that facts are copyrightable nor that books are not. If you used all the facts to reproduce a printed copy of the book, that would clearly be copyright infringement. But if you collected and used all the facts only to solve the book code, not so much. Interoperability is solving the book code, not reproducing the book. Function, not expression.
And it has nothing to do with publication vs. secrecy because that's a copyright thing. Facts are facts whether you intended anybody else to know them or not.
Copyright is the thing that applies to works of authorship, like short stories and music. You can't copyright a fuel pump for a jet engine. You can't copyright function. That's patents, not copyright.
Software is somewhat unusual in that it's at the same time a work of authorship (code, copyrightable), and a set instructions for a machine to interpret (functional), and pure mathematics (facts about the universe, not subject to patent or copyright).
But an API is at the intersection of the functional part and the factual part. What distinguishes a literary work from a fact is that the literary work leaves room for creative expression. A copyright on an expression of a fact isn't a copyright on the fact itself, because someone else doesn't have to use your expression. They can create their own expression, so you having a copyright over your expression doesn't exclude them from using or conveying the same factual information.
When someone creates an implementation of an API, the API itself is a fact about how to interact with implementations of that API. There isn't any other way to interact with other implementations, so there is no room for creative expression in that aspect of a compatible implementation, so there is nothing there to copyright. You have to use the same API for entirely functional reasons or it's not compatible. And you can't copyright function.