It's important to note what the ruling actually covers. I'll borrow from this good summary on Law.SE
- For acts within the President's "exclusive sphere" of constitutional authority (also referred to as "conclusive and preclusive" authority), President has absolute immunity from criminal prosecution (pp. 6-9).
- For "official" acts that are not within that central core, (“acts pursuant to an express or implied authorization of Congress,” or in a “zone of twilight” where "he and Congress may have concurrent authority"), the President does not have absolute immunity. Instead, here the President only has presumptive immunity from criminal prosecution (pp. 9-15). For such acts, the President is immune from criminal proseuction "unless the Government can show that applying a criminal prohibition to that act would pose no 'dangers of intrusion on the authority and functions of the Executive Branch'" (p. 14).
- For unofficial acts, "there is no immunity" (p. 15).
Rekesoft is right in pointing to Obama as a case where the President unilaterally killed a US citizen without any due process. That having been said, the person in question was Anwar al-Awlaki. In this case, the man might have been a US Citizen, but he was living in a foreign country and actively fomenting terrorist sentiments. That doesn't apply to a lot of people. It's arguable that killing someone who is encouraging violence against Americans on foreign soil is an official act.
Let's take a look at a more pragmatic case. A quote by Trump himself
"I could stand in the middle of Fifth Avenue and shoot somebody, and I wouldn't lose any voters, OK?" Trump remarked at a campaign stop at Dordt College in Sioux Center, Iowa. "It's, like, incredible."
Assume, for the sake of argument, that Trump actually did this while still President. As we've seen in the campaign finance case, Trump would be subjected to state laws about guns as well as attempted or actual murder. It would also be hard to argue this was an official act as President.
Let's pivot to Sotomayor's example. This is the full text of the ruling. (page 29)
The President of the United States is the most powerful person in the country, and possibly the world. When he uses his official powers in any way, under
the majority’s reasoning, he now will be insulated from criminal prosecution. Orders the Navy’s Seal Team 6 to assassinate a political rival? Immune. Organizes a military coup to hold onto power? Immune. Takes a bribe in ex-
change for a pardon? Immune. Immune, immune, immune.
The problem for Sotomayor is that Trump is still under Federal indictment for acts taken while President. The ruling only specifies that Presidential immunity actually exists, not how much is covered by it. How much of the three Federal indictments remain is something to be sorted out by courts (and SCOTUS left considerable wiggle room). If Trump were as immune as she claimed, the indictments would have been thrown out. Thus a President can still face charges after leaving office (something long established by Gerald Ford pardoning Richard Nixon).
Both the Seal Team 6 assassination and coup examples fall outside the Article II "core" powers. Moreover, the people who would have to carry out such orders would not share in any immunity claims. Being given an order by a President does not automatically make said order lawful. In the My Lai massacre, military personnel were charged with crimes (only the commander was found guilty). Both hypothetical orders could be considered illegal (Law.SE has a good discussion on the legal ramifications)
But the greatest torpedo to Sotomayor's dissent was in the ruling itself (starting page 39, some notes trimmed for brevity)
Coming up short on reasoning, the dissents repeatedly level variations of the accusation that the Court has rendered the President “above the law.” As before, that “rhetorically chilling” contention is “wholly unjustified.” Like everyone else, the President is subject to prosecution in his unofficial capacity. But unlike anyone else, the President is a branch of government, and the Constitution vests in him sweeping powers
and duties. Accounting for that reality—and ensuring that
the President may exercise those powers forcefully, as the
Framers anticipated he would—does not place him above
the law; it preserves the basic structure of the Constitution
from which that law derives.
The dissents’ positions in the end boil down to ignoring the Constitution’s separation of powers and the Court’s precedent and instead fear mongering on the basis of extreme hypotheticals about a future where the President “feels empowered to violate federal criminal law.” The dissents overlook the more likely prospect of an Executive Branch that cannibalizes itself, with each successive President free to prosecute his predecessors, yet unable to boldly
and fearlessly carry out his duties for fear that he may be next.
Assuming that either Sotomayor scenario ever happens, it's unlikely a Federal court would read this decision and assume that a political execution via Presidential power is subject to Presidential immunity (especially if Congress were to impeach and remove said President).