Since you imply that you're not an American, I'm going to pretend that you're not a troll and that you don't actually know this stuff. Yes, the president decides who is a threat. There's a
longstanding tradition of the president unilaterally authorizing military force, the United States has only formally declared war six times in its history and most (not all) other military actions undertaken by the US have happened on presidential authority. This is not always because the president is overstepping himself - congress has tacitly, even explicitly, approved of this authoritarian approach on multiple occasions, in particular the
Authorization for Use of Military Force Against Terrorists of 2001 which gives the president the authority to use all "necessary and appropriate force." This is the bill under which the justice department is claiming the strike on Anwar al-Awlaki was authorized.
The "gun" that Anwar al-Awlaki was holding was the planning and direction of new attacks against the United States. This is in TFA. It suffices for the authorization of force that the justice department and the president came to the conclusion that he was a threat. Not that he
might be a threat in the future, he wasn't killed because they were worried that he might
start planning attacks. Police officers are indeed allowed to decide in cases such as that whether a criminal will get a trail. Or, to be more accurate, police officers are allowed to determine situations where a criminal
will not get a trail. To return to this previous example: when a suspect is pointing a gun at a police officer the officer is authorized to come to the conclusion that capture is infeasible and that a trial will not be possible. The infeasibility of capture was also part of the justification for the strike on al-Awlaki.
Your implication that this is unusual, that the United States is the only country which authorizes its law enforcement to use lethal force, is way off base. However, I will certainly agree that the endless march towards authoritarianism that our country has been on is detrimental. This was made abundantly clear by our last president, under whom such sweeping powers as the aforementioned Authorization for Use of Military Force Against Terrorists was passed. That said, while I don't know enough to have an opinion on whether the strike on al-Awlaki was justified, I'm not so naive to say that all lethal actions should be forbidden in lieu of a trial. The fact that this particular one is being trotted out as an example of overreach while so many thousands of others are ignored is simple partisanship.