"The people dead did not choose to die. They were killed by someone. And that person killed people and intended to kill people. By our society's definition, this person is mentally ill- they are ill because they have decided to kill people when their own life is not in imminent danger."I guess all those soldiers who invaded Iraq, for example, were mentally ill, as were the politicians who ordered them to. As were all those involved in the many other invasions of other countries when they themselves weren't in any imminent danger.
Same goes for guards who shoot to kill escaping prisoners and police who shoot to kill people to keep them from killing others while their own lives are not in danger. Then there are executioners who legally kill people sentenced to death by a court of law. All of these people must be mentally ill, by your definition.
You should distinguish your definition from society's definition, because by society's definition all of these people are not mentally ill. In fact, society often rewards them with honors and praise, calling them heroes or at least paying them for their work and legally protecting them from prosecution for the killing they do. The suggestion to lock up such people in mental institutions because they're "mentally ill" would be considered laughable, insulting, and not worthy of serious consideration by the vast majority of society.
All of this is not to say that any of the above are morally equivalent to the killings that were perpetrated in this tragedy, nor is this to claim that the perpetrator is not mentally ill (it's for psychologists to decide that), but if the perpetrator is mentally ill then they can't be branded as such merely because they "killed people and intended to kill people.. when their own life is not in imminent danger" without also branding as mentally ill all those mentioned above.