Okay, my rough impressions offhand, after paging through the first part of the player's guide, is that the main reason military/DoD professionals are requested as players (aside from the point of the game being to train such people along with related State Department personnel), is because the game uses a bunch of contemporary acronyms and terms that insiders would be familiar with already, although the game rules do spell out what these are supposed to mean.
As a practical matter, anyone familiar with moderately complicated strategy games in modern settings (or even semi-modern settings, going back as far as let's say Napoleonic times) should be able to learn to 'translate' these concepts into gameplay we're familiar with. The rules are kind of more for explaining (overtly 'simple'!) strategy gaming in terms Defense/StateDep professionals will understand and relate to. Players don't even have to read the player's guide or rules, as long as the Facilitator is familiar enough to explain what's going on.
Example:
In Hedgemony, players may spend resources to do the following: Ø Posture or employ forces to accomplish some objective Ø Procure new forces (i.e., buy force structure, capacity) Ø Modernize existing forces Ø Improve specific force capabilities Ø Improve a nation’s capability or capacity to modernize forces Ø Sustain or adjust force readiness (U.S. player only) Ø Take other direct actions that may increase the players’ Influence.
Resources are generated at certain rates each turn, set by the scenario designer for each Player Faction, and can carry over to future turns (but can't be spent at a deficit, which is kind of hilarious since the goal is to simulate US State Department planning.

)
There are chits which get placed on map areas, and everyone has cards from various decks, including hidden hands of cards per turn, to play. Aside from personally defined Player goals (written out pre-game after learning the starting conditions), players are trying to score Influence as victory points.
So far I don't see any reason for seasoned strategy gamers to worry much.

Not only count me in! -- but I'll also poll around outside Grogheads to see if other strat-gamers may be interested in being Players (or joining Player teams).