Killing bin Laden Was Not Murder
Murder is commonly understood to be the unlawful or wrongful killing of a person. While killing bin Laden was definitely the killing of a person, whether or not that killing was murder turns on whether the killing was unlawful or wrongful. While what is legal and what is moral can and do diverge, in the case of murder, I would say that the law and morality dictate roughly the same things. The analysis of the issue will proceed as such.
If the killing of bin Laden was authorized by law, then it wasn't murder. For example, killing bin Laden may have been authorized by the laws of war. Bin Laden can be viewed as a combatant engaged in armed conflict with our country, and killing him was a legitimate action in the course of putting an end to that conflict.
One can always justify the killing of another through the doctrine of self defense. The killing of another is justified under a theory of self defense if the killing is reasonably neccessary (or seemed reasonable neccessary under the circmstances) to prevent death or severe bodily harm to yourself or another. In bin Laden's case, he participated in the killings of thousands of people to accomplish his political goals and vowed to continue exploiting those tactics to further his political agenda. In the bigger picture, killing him was necessary to prevent the further deaths of innocents. On the smaller scale, in that room, killing bin Laden may have been necessary to ensure the safety of the SEAL team. As long as the person pulling the trigger thought killing bin Laden was reasonably necessary to prevent death or severe bodily harm, the killing was legal. He could have had concealed weapons or explosives on him. It's not inconceivable considering the tactics his organization has used. Killing bin Laden with that knowledge seems perfectly reasonable.
No Process Was Due to bin Laden
Due Process is the idea that the accused should be afforded certain minimal rights when tried and punished for crimes. At a minimum, the accused should be given notice of the charges against them and be afforded the opportunity to defend or dispute those charges. Basically, the accused should be told what they're accused of and have the opportunity to disprove those allegations. The reasoning behind Due Process protections is to ensure that the govenment treats people fairly and does not act arbitrarily (doesn't do whatever it wants for no legitimate reason).
In the case of bin Laden, he was accused of masterminding the September 11 attacks. Bin Laden was clearly aware of these allegations, because he did not dispute these accusations, rather he proudly took credit . . . on tape . . . multiple times! Would a trial really have afforded him any more due process? No, we would have just played a bunch of his mix tapes and he would have easily been convicted. We knew we had the guy who did it, the guy knew we thought he did it, and he even said he did it . . . a lot. Maybe the the letter of the law wasn't followed in regards to Due Process, but the spirit and purpose of the law seems to have been sufficiently served. In any event, Due Process is not required by the laws of war or the doctrine of self-defense.