> how is assassination an official act?

In the majority's opinion they stated that any act carved out by the constitution for the president is an official one.

The constitution establishes the president as the commander in chief of the armed forces. If the president orders a member of the military to assassinate an individual, he's exercising his role as the commander in chief, an official act, and is thus criminally immune.

The slightly longer form also includes that the majority held that for official acts, a president's motives can't be probed by the courts, so whether the president ordered Seal Team 6 to murder a political rival for self-interested reasons, that it was an official act is the only thing that need be considered.

If Lincoln had a Seal Team Six, and ordered said team to take out Jefferson Davis, would Lincoln have been open to prosecution, or immune as he had been undertaking an official act as commander in chief?

That's the problem. The ruling provides no guidance whatsoever, so as long as a President can make the case, it's an official act.

I don't understand how you could not believe this under the majority opinion. The constitution is very clear that supreme command of the armed forces falls to the Commander-in-Chief. The President. It must follow that when the president directs the armed forces he is performing an official action that is exclusively given to him via the constitution. If that is not an official action, then what is? There is nothing in the constitution directing how the president should direct the armed forces. And it follows from that if its an official action then he is immune.

And she'll be on the minority side. Case decided, six to three, and she gets to write another dissent that will be ignored.

Bad logic.

Is someone more or less likely to perform such an act if there's a possibility of legal consequences? If not, then we don't really need courts at all, do we?

The fact that the courts have explicitly legalized these blatantly criminal acts is what gives the military the cover and the imperative to dutifully carry them out.