From the text, "GDP per capita" is used as a very rough proxy to efficiency. The idea seems to be that if you have a lot more GDP per capita than average then you're probably also getting better potential military value per dollar of GDP than a country where most of it goes to subsistence or other expenditures that aren't optional and hardly contribute anything to a war effort.
Another way to view this metric is as Population * (GDP/capita)^2. That is, a statement that military effectiveness per unit population increases superlinearly with economic development. Something like this probably does hold, though not necessarily with specific exponent 2.