Put simply game philosophy is a unified cohesive conception of what the game is and how it is to be played.
Officiating is the practical adjudication of the game philosophy. The referees, applying the rules (which define the game's elements & actions) oversee the play of the game to assure it reflects the game philosophy as accurately as possible.
Um, maybe so, but what's the point of all this jibber-jabber? I mean we've got a game already, right?
Right, sorta. Yes, we have a game already but if you take a moment to think about how we got the game we have maybe you'll see a value in trying to think about the game divorced from the baggage of our history. (Okay, maybe that's not completely possible but there is a virtue in not having the past overly influence or color one's thinking.) So far competitive paintball is largely composed of remnants of the earliest paintball played, a few fresh ideas and the momentum produced by technology & industry profit. Not exactly Frankenstein's Monster but there is a parallel. We have failed to take control of our sport by creating a foundation for its future development based on a shared philosophy of the game. As a consequence the game has had a kind of life of its own with changes being made piecemeal as a response to changing circumstances.
Not sure? Why do we shoot ramped and/or capped guns? Because rules were changed when the industry produced such guns and the hoppers capable of feeding them--and because they were popular. Why do we play the Race 2 variant of xball? (The most teams ever at WC featured 10-man play.) Why are the bulk of penalties based on removing players from the game? Why are field layouts mirrored halves or symmetrical?
At this stage competitive paintball probably won't end up as a game played from a clean slate conception so how does game philosophy make a useful difference today? New ideas breed new possibilities, new possibilities hold the promise of improving the game. Or making it worse. Or bringing about any number of unintended consequences. A shared game philosophy would mitigate the risk involved in making changes because every change would be considered against the standard provided by a game philosophy.