For some reason I'm just not following this story. Why should anyone care whether or not Goodell was asked to delay punishment? Correct me if I'm wrong, but isn't this whole thing about the players accusing Roger of punishing them without adequate, or really any evidence at all? Isn't Vilma's lawsuit about Defamation? This copy (what a surprise, another copy of something and not an original) of whatever they claim the NFLPA asked for has absolutely nothing to do with anything in my eyes.

I am no lawyer, but as I understand it:
Goddell made statements about the players when he issued punishment for the coaches in March, such as "they embraced [the bounty [program]", and named Vilma and Smith as the leaders. But then, he made statements in April about how the investigation was still on-going and he was still considering evidence to arrive at a decision on what the punishments should be. If he indeed had made up his mind in March and was ready to hand out punishments in March before the investigation was concluded in late April, it shows that he had a prejudice against the players, and therefore was not an impartial arbitrator either on handing out original punishments, or the appeals. It also enforces Vilma's claims of defamation, as any statement made before the investigation was concluded would be considered slanderous.

...but I am also curious as to what the judge thinks of the so-called evidence provided by the NFL about the bounties, and not just some letter asking for a delay.

If I remember correctly, she said the evidence is "borderline ridiculous".