Do you have a problem with that?
"Space," picking an example at random, is defined as "A medium like the land, sea, and air within which military activities shall be conducted to achieve US national security objectives."
Space has been used for military activities for over 40 years and not just by the US. Military activities is a very broad term. GPS satellites are performing military activities by providing precision timing and navigation services. They weren't put up there (by the US military) just for fun. Same for the military communications, ISR, and other space systems.