I believe to those who believe Barack Obama is not qualified Constitutionally to hold the office of POTUS, he is recognized as de facto President in posse and as de jure President in posse. That doesnt fit neatly onto an envelope.
Nor very likely would having addressed a letter as this man did be recognized as an admission against interest before any tribunal.
There is an established protocol for addressing the man who occupies the office of POTUS. The addressing of the letter followed that protocol. Even those who do not believe Obama is Constitutionally eligible still address him as “Mr. President.” It’s just proper etiquette.