No, no it doesn't. Simply put, there was no public comment made by any member, past or present, of the Minnesota Wild organization in regards to going after Parise in free agency. That really is the only way that the league will automatically go after the team for tampering.
Also, he said it on radio and is a credible source, an investigation has to happen.
Sure, the Devils could file tampering charges & try to convince the Commissioners office to investigate. Realistically, the only way that happens is that Parise ends up signing with the Wild straight out of the gate on July 1st. And if all the league can find is that a 72 year old former GM of a completely different club, popped off at the mouth during a radio interview, nothing will come of it. Unless they can find hard evidence that there was a distinct plan to leak info out to the public (say like in an internal email chain) through Nanne or, like in the case of the Blues tampering w/ Scott Stevens when he was an RFA years ago, the actual existence of a contract that was drawn up & discussed with Parise's agent prior to July 1st, the whole thing will go nowhere.