Something really needs to be clarified. The OP uses the terms "round," "match," "battle," and "duel" without properly defining all of them (or using them in a contradictory manner). Here's what I gather:
SPECIAL: whenever one of the Twelve loses a match (not a whole battle: for instance, this applies twice if he has won 3-2 this round), he loses 2 Upgrades.
According to this, a battle is 5 PvP games, and a match is a single PvP game.
VICTORY: if a Barbarian wins a match, his opponent is killed (eliminated).
According to this, using the interpretation taken from the Twelve SPECIAL text, if a Barbarian wins a single game out of 5, the opponent dies. Is that really what was meant?
Matches are best-of-five. The first player who wins 3 individual duels, wins the match.
According to this, a match is 5 PvP games, and a duel is a single PvP game. This is in contradiction to the earlier quote.