Iturrizaga Bonelli's early chess career saw him participating in several international youth tournaments, with noteworthy success in the World Youth Chess Championship and Pan American Youth Chess Championship. As an adult, he participated in numerous chess tournaments around the world. His first major victory was at the Venezuelan Championship in 2005. Thereafter, he notably won the Iberoamerican Chess Championship in 2008, and competed in the Chess World Cup 2007, 2009, 2013, 2015, and 2017 editions.
In 2019, he moved to Spain and started playing for the Spanish Chess Federation. Later that year, he won the Spanish Championship. Iturrizaga Bonelli also represented Venezuela at the Chess Olympiads from 2006 to 2018, contributing greatly to the team's performance. He has continued his active participation in various tournaments, solidifying his status as a formidable chess player.