It is unclear whether WINE is infringing copyright or if it can rely on a fair use defense.
The CAFC held that:
that the declaring code and the structure, sequence, and organization of the API packages are entitled to copyright protection
In that light, if WINE had original content in the structure, sequence, and organization of its API, the CAFC would likely also find that it is entitled to copyright protection. However, because this issue is outside the scope of the CAFC's exclusive jurisdiction (this is a copyright issue, not a patent issue), the holdings are not binding in any other circuit.
Each circuit is free to review anew the copyrightability of APIs when such a case comes up. My guess is that this is the reason the Supreme Court declined to hear an appeal on CAFC's Oracle v. Google opinion.
To address your fair use question would be simply speculation, because fair use is always assessed case-by-case, and even in WINE's closest analogy (Oracle v. Google), the CAFC remanded the fair use question back to the trial court, and that question hasn't been decided yet:
we remand for further consideration of Google’s fair use defense in light of this decision