It may be that LFA was trying to correct a common misimpression that, because it was morally rigorous and enforced a strict honor code, it was also military in style. But it's also possible that this was just one of several categories or designations for prep schools of the period. For example, Thorpe Academy for Boys, also in Lake Forest, Illinois, indicated in newspaper ads that it was "Semi-Military . . . Uniforms worn" (Chicago Tribune, Sunday, 24 Jul 1921, page 77).
And, yes, $950 was a pretty penny in 1921. $1,000 in 1928 (a date I checked once) had roughly $15,000 worth of buying power in 2012 dollars. Not sure about the conversion from 1921 dollars to 2018, but it must be similarly impressive.