I think you are misinterpreting the question. The US Constitution obviously has no legal impact on the laws of Saudi Arabia. The question is whether the US government needs to follow the US Constitution when dealing with a non-US citizen on non-US soil.

There seems to be a precedent that US citizens have different legal protections from the US government while abroad when compared with non-citizens. That is why US citizens involved with Al-Qaeda, ISIS, or similar hostile organizations will occasionally receive a domestic trial in the criminal justice system while non-citizens generally only face military trials if anything.