So, you admit you made a choice that resulted in people dying. Thus, you killed them.
Wrong again. You fail both English and Logic.
Choosing to kill people is also known as 'murder'.
This sentence contains the explanation as to why you are an idiot. Choosing to watch someone be killed and choosing to kill someone are very, very different things. And so yes, choosing to kill people is known as murder, but not choosing to kill three people in order to save three hundred people is not known as murder, while choosing to kill three people in order to save three hundred people is murder. It may well be considered justifiable, but it is still murder. Unless, perhaps, you claim that you didn't think, and you just sort of moved of your own volition. In that case, it might well merely be homicide.
However, unless it is specifically, contractually your obligation to pull that lever to minimize deaths, it is not your responsibility to make that decision, whether it is even murder or not. Which it is, but only if you pull the lever, and cause the deaths of three people who would have lived if you had done nothing but observe.