First, taller soldiers, especially during the less prosperous times of the early 20th century, may have been physically stronger and more fit, as well as possibly genetically and developmentally healthier. So they might have been better able to resist diseases and wounds sustained during combat, when they might have killed their shorter and less healthy comrades.
Second, height is known to be correlated with intelligence. While scientists disagree on why taller people are more intelligent than shorter people, the fact that they are is beyond dispute. If taller soldiers on average are more intelligent than shorter soldiers, then they may be expected to achieve higher ranks within the military. Even though the sample used in the study of the British soldiers in World War I includes only enlisted men and noncommissioned officers and excludes commissioned officers, it is possible that taller and thus more intelligent soldiers were able to climb the ranks of noncommissioned officers to such ranks as lance corporal and sergeant, and were able to avoid the most dangerous combat situations because of their relative rank. Alternatively, taller and more intelligent soldiers might have been better able to fight successfully in modern wars. For example, a surprising number of British soldiers survived World War I by deserting. They may have needed higher intelligence to desert and avoid court-martial successfully.