It lacks any form of military engraving on the dial or caseback so it's impossible to say if it truly is a military piece. Manufacturers made this style of watch during the War so that soldiers who were not issued a wristwatch as standard equipment could own a reliable timekeeper, but the same style would have found its way into general retail too. Of course, given the style and period of production, we can speculate it was owned and used by a soldier, but that's all. You should contact Longines and ask for their archive extract, if they say it was delivered to a military base then you have your answer. However, their records are quite scant for their watches sold in the USA like yours.
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