I am not saying I have an answer for that.
This is not a First Amendment question because in this case a corporation that regards themselves in the business of entertaining people has decided that they don't want to risk releasing this movie right now. Yes, they are caving to a threat, but the movie is their property under Copyright to do what they choose, and they choose to not show the movie as of now. They could have just shown the movie, shown the movie but put metal detectors and guards up around the theatres, or maybe even demanded protection from the threat by the government.
There is a broader embrace of free expression in our society going beyond the First Amendment, and caving against the threat undermines free expression. But there is no law against giving in to blackmail -- there are only laws against taking justice into your own hands in acting against a blackmailer. We only wish, sometimes, that the Westboro Church, the book-burning Florida cleric, and the Egyptian movie-making dude would give in, and this wishing out loud by Administration officials gets pushback regarding First Amendment concerns, but there would be no wrong if those people had caved in light of the threats facing their free expression.
So (if presumably it was North Korea) threatened violence within our borders, they haven't violated any law because they are not under US law. On the other hand, such a threat could be construed as an act of war, submitting to such a threat diminishes our honor to the extent that free expression is one of our cherished values, and nations have gone to war over questions of honor -- many times. In other words, to cave humiliates us as a nation in our own eyes, which by definition, is a matter of honor.
Do we want to fight back for our national honor? Does honor, or the principles of honor in this dispute with North Korea rise to the level of risking lives in a war? I am not saying there is a simple answer, but when people say that going to war over "honor" is competely stupid, this example should come to mind. That North Korea effectively has veto power over what is shown for movies in US theatres is a question of honor (we will attack you if you show this movie) -- no one has died (yet), but do we want to live this way? But on the other hand, is a dumb Seth Rogen pic a cause worth dying for?