The Gifts are the fiefdoms of the Night’s Watch, and were specifically ceded by the Starks of Winterfell to the Night’s Watch so that the incomes from those lands would support the mission of the Watch. As the Night’s Watch is a neutral, independent organization, so too are its lands neutral and independent.
As for the King on the Iron Throne, while the Night’s Watch receives royal patronage in the form of funds, recruits, etc., it’s not directly under the king’s control either. Hence why Tywin couldn’t order the Watch to elect Janos Slynt but instead tried to use economic pressure, and why Cersei was arranging for Jon Snow’s assassination rather than execution.