He became an International master in 1994 and received his GM title in 2006. Gonzalez Zamora has experience in competition play at the Chess Olympiad, where he first competed for the Mexican team in 2002. He has since participated in several subsequent tournaments. He also played in the FIDE World Chess Championship 2002 but was eliminated in the first round.
Gonzalez Zamora additionally competed in the 2005 and 2007 World Cups, though he did not manage to progress beyond the first round in either event.