Me too. I know it's somewhat hyperbolic, but could this ruling make it possible for the POTUS to order a SEAL team to kill a US citizen?

I don't think so. Not only does the President lack any authority to do that, but in fact an extrajudicial killing would be clearly unconstitutional. It wouldn't be an official act within his Constitutional authority (the innermost circle), or an official act to which a presumption of immunity would apply (the second circle). Seems like that would pretty clearly be an unofficial act.

Plus, don't forget that the immunity being discussed would only apply to the President. So matter what outcome was reached with the President (again, I think under this ruling he would have no immunity), everyone else would be subject to prosecution. So the shooter would be guilty of first degree murder, as would (probably) all of the other members of the Seal team that participated in the effort. Probably everyone in the chain of command between the President and the Seal team would be guilty of conspiracy to commit, in addition to a host of other lesser crimes.