I think that it means they lose exclusive rights to the TEAMS, but keep exclusive rights for the players. Since the players are all part of the NFLPA, and I don't think this ruling had anything to do with the NFLPA.
This ruling only says that it is possible for the NFL teams to break the antitrust laws, not necessarily that they did. Now this case has to go back to the lower courts that dismissed it summarily on the grounds the NFL was one corporation to litigate it.
I imagine any other contractor would be able to sue likewise using this ruling to avoid getting its case dismissed summarily on the same grounds.