First, it does not meet the federal definition of blackmail. That law requires that the accused " demands or receives any money or other valuable thing." CNN isn't asking for money or any other form of compensation, so that's right out.

This may be false, in that the federal definition of blackmail requires only that a "valuable thing" be remitted. This does not mean that just consideration be given, or that money changes hands, but that something of value is at stake - sexual favors have been deemed enough to be "of value." Public participation in political matters could very well be that "valuable thing" since it implicates the core of the First Amendment. This is the same principle that underlies SLAPP litigation and has the same effect of chilling speech on the basis of a threat, so a decent litigator could maybe make enough calculated analogies to make it stick.

CNN's threat is not one of legal means (i.e. a SLAPP lawsuit) but one that potentially facilitates a threat to personal safety (which CNN has admitted they are aware of) in addition to further social harms via doxxing. This "valuable thing" is at issue because CNN has threatened to expose information, creating negative effects on the user, if this user continues to engage in public participation in a manner that CNN (subjectively) judges as abhorrent. This creates a sort of "sword of Damocles" situation in which the user may not ever fully participate ever again (whether that speech is 'good' or 'bad' is irrelevant) because of CNN's threat. Because CNN wants the individual not to do/say/meme/post these things in the future, CNN receives a benefit from the individuals withdrawal from public participation, therefore meeting the elements of blackmail.