Are we still trying to win anything?

Is it just me, or are some of the justices claiming that anyone who is in the custody of our military anywhere in the world has the right of habeas corpus?

I haven't seen anything in this about war powers. Isn't the detention of illegal combatants part of the president's power as CinC? I'm no Constitutional scholar, but it seems like it might be better to just shoot these people instead of taking them captive if they're going be given an immediate appeal to the U.S. Courts.