7 games need to be played to determine the tournament winner.
Work Step by Step
Eight teams are competing in the tournament. Any team that loses a game is eliminated. This means that after 1 game, there is 1 less potential winner. We have the real winner when there's exactly 1 potential winner left, or rather when all the other teams are eliminated. We have 8 teams, therefore for there to be 1 left, we need to eliminate $8-1=7$ teams. To eliminate 7 teams in this tournament, there has to be exactly 7 games. 7 games need to be played to determine the tournament winner.