Maybe it's because he's pitching for a team outside his native state of New York.
Maglie started his career with the New York Giants in 1945. He pitched in 13 games that year before going to the Mexican League from 1946-49. That's kind of weird.
Then in 1950, he returned to the Giants where he stayed until 1955. He then moved on to Cleveland where he pitched for parts of 1955 and 1956.
Then back to Brooklyn where he would pitch for parts of 1956 and 1957. Then he went on to the Yankees where he pitched for parts of 1957 and 1958. He finished the 1958 season in St. Louis.
Come to think of it, that's probably the look of exhaustion.