It's a confusing ruling, decided mainly on procedural grounds. The district judge ordered the files released, before the case was over. The government appealed, and the Court of Appeals said that, because the case wasn't over in the district court, it (the Court of Appeals) had no jurisdiction to overturn the district court. The Supreme Court held, 7-2, that the Court of Appeals did have jurisdiction to review the district court's order. The opinion for the Court (written by Kennedy, joined by Rehnquist, Stevens, O'Connor and Breyer) decided that jurisdictional issue and nothing else. It has the effect of sending the case back to the Court of Appeals without telling it how to decide whether or not to release the files (but effectively postponing any release until after the election).
Stevens joined that opinion but added a concurring opinion hinting that he thought that some, but not all, of the files should be released.
Thomas (joined by Scalia) concurred in part, saying that (a) the Court of Appeals does have jurisdiction, and (b) the district judge was wrong and none of the files should be released.
Ginsburg (joined by Souter) dissented and said that the Court of Appeals had no jurisdiction.
Did the district court ever allow the rest of the case to be heard? If not, I can see the AC kicking it back down again, instructing the DC to finish the case & to make an additional ruling.