The correct way to interpret this is that the Court of Appeals has to find that Judge Nelson acted "unreasonably" or "abused her discretion" in issuing the ruling. In other words, her judgement has to be unsound, and this is highly unlikely.
It's essentially the same principle and philosophy used by the Officials on the field when reviewing challenged plays during a game. They must find clear evidence of wrongdoing or error, in order to overturn the original call.
There's a nuance I would add. There are three "standards of review" in appeals. First, questions of law are reviewed de novo. De novo basically means the review is brand new. The court gives no deference to the trial court. To continue your instant replay comparison, the call on the field doesn't matter, just what the video shows. Second is clear error, which doesn't apply here because there weren't factual findings. Last is abuse of discretion.
While it's true that a decision to issue an injunction is discretionary and thus reviewed for abuse of discretion, when an injunction is based on a
legal decision, the court of appeals will review that legal analysis de novo and then decide whether an injunction is still warranted.
Here, there is a significant legal question embedded in the court's analysis. (Actually, there are three, but one of the three I think will get more traction than the others.) Specifically, she interpreted the words "arising out of" in the NLA very narrowly. The court of appeals won't give her any deference on this issue.
Also, FWIW, the NFL filed its appeal last night. Contrary to reports yesterday that Nelson denied a stay of her order pending appeal, she didn't. (She couldn't until there was an appeal.) Now that there is an appeal, she will be asked to stay it. She will probably say no, but she might give the NFL some time to implement her order. Once she issues her ruling, they can ask the 8th Circuit for a similar stay pending appeal. (Actually, they can do it earlier if she takes too much time, but that's usually not good form.)