Not a fan or admirer of Bezos by any means, but a threat of “stop doing X or we’ll publish embarrassing photos of you” does seem a bit like blackmail.
Not Blackmail, it’s Irony.
What exactly did the National Enquirer request?
Telling a prominent person "if we don't get your side of the story, we'll have to go public with what we have already" is a well-established way to get an interview when one has been refused.
I think they are saying, “we have more damaging stuff. stop lying about us, or we will be forced to release the damaging stuff to clear our name.”
That’s not blackmail. That’s just a straightforward call to stop the BS.