In this case the opposing party(Goodell) and the arbitrator(Goodell) were one in the same. The first court ruled on the dishonesty and fraudulent practices of Goodell the arbitrator.
This court ruled:
Even if an arbitrator makes mistakes of fact or law, we may not disturb an award so long as he acted within the bounds of his bargained-for authority, two of the judges on a three-man panel ruled. Judge Robert Katzmann dissented.
They as much as said Goodell did not follow the law and was dishonest but by 2-1 the judges said that it does not matter.
It's really pretty simple. The Union signed a collective bargaining agreement that gives Goodell incredible authority. So if he's judge, jury, and executioner, that's perfectly fine as long as the Union agreed to it. Which, they did.