Harming the blackmailer is simply a proxy for "this isn't a course of action the blackmailer would otherwise engage in; they do it only for its blackmail effect"
I would say that if Baron truthfully tells Countess "I have been offered $100,000 for your letters by the Daily Tabloid, but in honor of our friendship I will give you the chance (which I hope you reject) to purchase them instead for only $50,000", I think this still counts as blackmail, as a matter of ordinary usage. So I agree with Decius in this respect.
For game-theoretic purposes, however, it might be worthy to restrict the definition the way you do, since it calls for a different response strategy: If Baronet also has letters incriminating C...
My blackmail posts have generated some interesting discussion, so I'm just creating this one so that people can post examples of behaviours that they think are either clearly blackmail, or clearly not blackmail, or something in between.