The OP asks when threats are real, and then later on there is talk of when threats are justified. Neither have anything to do with a third question which is what constitutes a threat. This latter question basically calls for a list of criteria delimiting the speech acts that would be threats. A threat is a statement in which a person reveals to somebody his or her intention to do something bad to that person in the future. Of course, whether something is ‘bad’ is open for discussion - I’ll kill you may not be a threat to a suicidal person or made by a suicidal person.
Others are more qualified to define a threat than me. The point is, however, that a statement may or may not meet the definition and be a threat but this is a totally separate discussion from a) whether this threat is justified (whether visiting the announced bad on somebody or even announcing this possibility is the ethical thing to do) and from b) whether this threat is real (i.e. whether the person making the threat can be trusted to make good on his drunken boast).
Because it’s not a threat coming out of thin air. Nor is it based on an unreasonable request from the “threatee”. Threatening to hurt someone if they listen to a particular radio station would be unreasonable. Threatening to hurt someone (or should I say forewarning) if they ever commit a crime against you should be totally allowed. According to some of the cites, it appears that in some jurisdictions it is allowed.
Maybe we’re (or I am) splitting hairs here. I call something a “threat” only when it is illegal. The forewarning type statements I described (when legal in a jurisdiction) ought not to be referred to a threat.
But I believe my OP has been answered since some have been kind enough to cite actual definitions of a threat.