The purchasing power is the concept that refers to the fact that costs are different in different countries. For example, if we compare Canada, which is a well-developed country, to other countries like India and China where military personnel pay is lower than in Canada, the purchasing power of a U.S. dollar spent in both countries does not buy you the same military capacity. That's probably what is referred to in the study you quoted.
There are also the effectiveness of the spending itself, how well integrated the different branches of the military are and the mix of spending between pensions and benefits, personnel, equipment and infrastructure.