SoG = Shades of Green, the military hotel located on Disney property
Since you have to show a military ID to buy park tickets at SoG, you do not need to then show the ID again at the park. The only exception to this would be the ones that specifically say you have to activate at the park, like the Disney Salute tickets.
You also need to show an ID at the park gate if you are getting something through Waves of Honor.