In the 2016 42nd Chess Olympiad held at Baku, Azerbaijan, Torre played in his 23rd Olympiad, further extending his record, where he played on Board 3 for the Philippines. He played in all 11 games, the only Philippine player to do so, winning 9 games and drawing 2. He had a very high performance rating of 2836 and won the bronze medal for Board 3 just behind former teammate Wesley So of the United States and Zoltan Almasi of Hungary. He gained 46.9 Elo rating points increasing his Elo rating from 2447 to 2494. At the conclusion of the 2016 Chess Olympiad in Baku, Azerbaijan, Torre had already played 270 games with 103 wins, 124 draws and 43 losses for a grand total of 165 points (61.1% winning percentage).