I think it's pretty clear it is reset. The whole point is simply that when you play the troop it has some effect but later when redeploying that effect does not repeat. If the card is stolen and then played from scratch the effect happens again (only once).
I feel the wording "When first play" is referring to other cards that allow you to move a players troop from in play directly to YOU but still in play. In that case it would not trigger Pax as the troop already did that.
Everyone above has it right. You don't track whether a card has been played before or not.
Section G "The play of any Troop Card affects the Regime..."
Therefore playing a troop card will change the regime, regardless of whether the card has ever been previously played [and notwithstanding the word 'first' which was used to distinguish movement of the card already in play]