Whatever the signs may say, travellers are not legally or morally obliged to report threats to law enforcement. So the OP should be thanked for getting in touch with someone, even if he used the wrong channel.

What I don't get is the behaviour of the check in agent. She/ he overheard the threat, in fact was included in it, and chose to do nothing? This is an employee of the airport/ airline/ contracted ground services firm. His/ her obligations are much greater than a passengers.