The difference is that the concussion case was purely a matter of law. Deflategate, on the other hand, is a matter of contract. The "legally responsible exercise" of that power is a bunch of gibberish. The parties got the deal for which they bargained, and that included giving the Commissioner this authority. Had the parties wanted such decisions to be reviewable by an independent, outside arbitrator for "fairness" or "being responsible", they'd have done so. They didn't. The bargain to which they agreed should be enforced as written.
The truth is that the Union consciously made this deal to give the Commissioner that much power, and got other things in return during the negotiating process. The reason you do this is to avoid long litigation over disciplinary matters. This is a case the Supreme Court shouldn't even take, and if they do, it basically amounts to de novo review of arbitration decisions.