It looks like the NFL practices what it preaches...a Tweet makes it "more likely than not" that someone is going to do harm to the Commissioner.
Otherwise, I think someone at 345 Park has been watching too much Ray Donovan or has been binge-watching reruns of The Sopranos.
If the League has credible reason and evidence to believe that a Tweeter or Poster poses a threat to Roger, its only course is to refer the matter to the local police (if the threat comes from within DC, New York City or Goodell's home town) or to the FBI if it crosses state lines.
Otherwise, the League has no more rights than a husband or wife who thinks their spouse is cheating on them; they can hire a detective to gather evidence legally and, in this case, turn it over to the authorities.
I'd love it if they were caught trying to do anything illegal, though.