If Trump were to personally shoot someone on Fifth Avenue: Not immune. (Probably. Maybe.)
If he were to order the army to massacre thousands on Fifth Avenue: Immune. (Very clearly, under the decision.)
But from a constitutional perspective, the latter is the grave danger to guard against.
Professor Levy in your hypothetical the president would first need legal authority to order such a massacre before it would be considered an official act and thus exempt him from criminal prosecution, right? Where would this authority come from?
He is commander in chief of the armed forces. That Article II power isn't subdivided into particular tasks: send them to this place, kill those people. Moreover that's a *core* power, in the language of the decision; immunity is absolute, not just presumptive.
It has traditionally been assumed to be subject to *external* legal constraints, but the constraints don't arise from within the meaning of the power to be commander in chief. And those external constraints have been rendered null and void.