You are way off base. The film takes place 1951 to 1953. Stewart was born in 1908, so he would have been 43 to 45 years old when during that period. But Hollywood license takes age off people, so he might have been portrayed as a 38 to 40 year old. That is perfectly is consistent with both his rank in the Army Air Corps and the baseball position. By the way, he was portrayed as a third baseman in the film, not a pitcher,
There were lots of older pitchers, too:
Horace “Hod” Lisenbee was a right-handed pitcher who played his last game for the Cincinnati Reds at 46 years old. Retired in 1945.
Irvin Key “Kaiser” Wilhelm was a right-handed pitcher who played his last game for the Philadelphia Phillies at 47 years old. Retired 1921.
Philip Niekro was a right-handed pitcher who played his last game for the Atlanta Braves at 48 years old. Retired 1987.
Jamie Moyer was a left-handed pitcher who played his last game for the Colorado Rockies at 49 years old. Retired 2012.
True enough, but these guys are exceptions to the rule. Niekro was a knuckleballer so his arm lasted and lasted. Moyer threw a lot of junk, slow, slower, and slowest, so his arm never wore out either.
Another notable exception to aging out was Nolan Ryan, who somehow miraculously never lost his velocity and threw a no-hitter in his forties.