Zagorskis has competed in multiple World Chess Championships, advancing to the second round in the 2000 and 2002 editions. He has also participated in the European Individual Chess Championships with strong results. In the Chess Olympiad, he has represented Lithuania many times on both team and individual levels, and his performance helped the team achieve their best result (11th place) in 2002.

Zagorskis works as a chess coach and has a physical education degree. In 2013, he earned a doctoral degree in the field of sport science, becoming the world's first chess player to attain such a qualification. As a scientist, he focuses his research on chess players' fitness and the physiological aspects of playing chess. He has published several academic articles on the topic.

Apart from competitive chess, Zagorskis has made significant contributions to chess literature. He has co-authored a chess textbook that is widely used in Lithuania, as well as books on other aspects of chess such as "Chess Strategy" and "The Openings in Modern Chess". He's known for his refined intellect and strategic brilliance, and his playing style is described as flexible, assembling different elements harmoniously to form strong positions.