The Buenos Aires Rugby Union added: "The Board of Directors of URBA expresses its condolences for the death of the former player and current PF of the SIC senior team, Santiago Bourdieu, and accompanies his family, his friends and the club in this moment of sadness.".
The video, captured on Saturday afternoon, caught Bourdieu start running towards the "Spitting Cave" cliff edge on the American island of Oahu, near Honolulu.
Horrified tourists watched as the 28-year-old Argentinian sportsman, Santiago Bourdieu, jumped from an infamously dangerous spot in Hawaii.
The SIC released a heartbreaking statement after his shock death saying: "We share great affection [with] all the family and friends of Santi in this moment.
The 28-year-old also played rugby at the San Isidro Club (SIC) until last year, when he became a physical trainer.
