The article is about people trying to get top-paying jobs at "management consultants, investment banks and big law firms." "The disadvantaged" means people who are thought to be at an unfair disadvantage in getting these jobs, due to social or economic circumstances. Someone who did not get a college education... or even someone who got a college education at "State U." rather than an elite university... is at a disadvantage. However, the article says, having been in the military can give such a disadvantaged person a "leg up," by giving them other positive qualities they can point to.