That's a promise, not a threat, by Schelling's terminology. Once the movie start upholds her end of the bargain, the man has no incentive to keep his promise, and every incentive to break it.

Is there something game-theoretic about blackmail that makes it an identifiable subset of the group threats + promises? Note that Schelling also describes a negotiating position that is neither threat nor promise, but the combination of the two. And that's not exactly blackmail either. I suspect you could come up with a blackmail scenario that fits any of the three groupings.