It's simple really. It's not murder when someone in the military kills an enemy combatant. Murder is illegally taking another's life, and members of the military can legally kill enemy combatants. That's laid out in the Geneva Conventions and all of that.
The President is the commander in chief, so he doesn't need immunity to order some terrorists taken out. That's the way it's worked for nearly 250 years. Joe Citizen is not a member of the military and is not the president, so generally they can expect to get in trouble for that sort of thing.
The President can order some terrorists killed the same way a fighter pilot can shoot down an enemy plane, a soldier can throw a grenade into an enemy foxhole, or navy captain can order the shelling of an enemy position.
Also note that immunity here doesn't mean something is legal for that person. The act is still just as illegal as it has always been. It just means that the person who has immunity can't be prosecuted for it. And in the case of absolute immunity, can't even be charged for it, unlike things like qualified immunity where someone can still be charged and then can argue immunity as their defense the courts get to decide if it actually applies.
As such, a member of the military doesn't have or need immunity, because what they are doing isn't illegal. That also applies to the president in that sort of situation.