The chess opening, the Torre Attack is named after him - it is characterised by the moves (in algebraic notation) 1. d4 Nf6 2. Nf3 e6 3. Bg5.
Torre also introduced the Mexican Defence to chess theory in a match against Fritz Sämisch in 1925 in Baden-Baden, Germany. It runs 1.d4 Nf6 2.c4 Nc6. Torre later dropped this line, but it was never refuted. It is also known as the "Black Knight's Tango" (International Master Georgi Orlov wrote a book on the opening under this title). Since it may transpose into quite many known openings, it is not a compact opening and so perhaps not suitable for beginners, but its uncommonness means it has surprise value.