Na 39th Chess Olympiad nke emere na Khanty-Mansiysk na 2010, Torre na-arụ ọrụ na Board 4 maka Philippines ma kpọọ egwuregwu 7 ebe o nwetara akara 41⁄2 na mmeri 3, 3 na-adọta na 1 ọnwụ na ọkwa arụmọrụ nke 2460 nke bụ onyinyo n'okpuru ọkwa Elo ya nke 2489. N'afọ 2012, Torre sonyere na ihe ndekọ ya nke 21 nke Olympiad na 40th Chess Olympiad
na-agbaji ya tie na Lajos Portisch ẹkenịmde ke Istanbul, Turkey. Ọ bụ ya bụ onye na-arụ ọrụ na Board 3 n'egwuregwu Olimpik a. O nwetara akara 31⁄2 n'egwuregwu 7 site na mmeri 2, 3 draw na mmeri 2. O dekọtara ọkwa arụmọrụ dị elu nke 2611 na Olympiad a, dị elu karịa ọkwa 2469 Elo ya. N'afọ 2014, Torre na-arụ ọrụ ọzọ na Board 3 maka Team Philippines na 2014 Tromso Olympiad maka ihe ndekọ ya nke 22 na asọmpi ahụ. O nwetara akara 51⁄2 n'egwuregwu 9 na-ede 3 mmeri, 5 na-adọta megide otu ọnwụ. O dekọtara akara ngosi arụmọrụ nke 2527 wee nweta 9.9 Elo isi na Olympiad ahụ. N'oge ahụ, o nwere akara Elo dị 2438.