I'm going to say just for battle. "Gained" abilities are acquired by set-aside or "remainder of the game" abilities, other than Increase/Decrease which are defined separately. The word "gain" in this case is old wording based on the original definition of First Strike:
First Strike
First strike is a special ability that keeps a character from being defeated in a mutual destruction situation. Playing a card with first strike ability does not prevent the opponent from continuing to play cards in battle. After all cards are played in the Field of Battle, a character with first strike defeats the opposing character if the character with first strike has strength equal to or greater than the opposing character’s toughness. However, if a character has first strike but has strength less than the opposing character’s toughness, then resolve the battle normally and disregard the first strike ability. If opposing characters in battle both have first strike ability, the character who gained it first takes precedence.
