Zatorski is an alumnus of Skra Bełchatów. He represented the second team of the club from Bełchatów. In that time, he won two titles of the Polish Champion (as a cadet and junior). In 2008, he moved to AZS Częstochowa and debuted in the top Polish volleyball league – PlusLiga. In 2010, he returned to PGE Skra Bełchatów. He spent four seasons in Skra, winning two medals of the Club World Championship – silver in 2010 and bronze in 2012, silver medal of the Champions League, two Polish Cups (2011, 2012), and two Polish Champion titles in 2011 and 2014. On 6 May 2014, it was officially announced that Zatorski had signed a contract with ZAKSA Kędzierzyn-Koźle for the next two seasons. On 26 April 2016, he won his third title of the Polish Champion, this time with ZAKSA. On 2 May 2016, it was announced that Zatorski extended his contract for the next two seasons (until 2018).