How did the GWOT come to be known as the US longest war?

Actually, Korea and Viet Nam were considered proxy conflicts with the Commies and were hot portions of the Cold War. I guess directly involved is in the eye of the beholder. We were REALLY involved in the Cold War! Skip Cold War and conflicts that you mention and explain how US not directly involved in Indian War and if you only count the period of the Campaign Medal (25 years) it is still longer. Your chart says only fought outside US Territory, however, it lists the PI which were given to us by Spain in 1898 and therefore was a US territory during the PI-American war.
BTW, first US service member KIA was in NOV 1955 during attack on Bien Hoa AB. Ike sent the first troops there. That 9 years sooner than you have listed for hostilities.

MAJ Ronnie Reams - “BTW, first US service member KIA was in NOV 1955 during attack on Bien Hoa AB. Ike sent the first troops there. That 9 years sooner than you have listed for hostilities.”
Please refer to the bottom of the graphic, the 2. annotation.

Additionally, the first death was in 1956. (Blue on blue attack). The Biên Hoa attack occurred in 1959, where two of our service members were were killed.