Dzeinichenka represented Belarus at the 2012 Summer Olympics, where he competed in the men's 96 kg class. He defeated Egypt's Mohamed Abdelfatah and Estonia's Ardo Arusaar in the preliminary rounds, and eventually upset Albanian-born Bulgarian wrestler and heavy favorite Elis Guri in the quarterfinal match, receiving a total score of four points in two straight periods. He progressed to the semi-final round, where he was defeated by Russia's Rustam Totrov, who scored a total of four points in two straight periods, leaving Dzeinichenka without a single point. Because Totrov advanced further into the final match against Iran's Ghasem Rezaei, Dzeinichenka automatically qualified for the bronze medal match, but narrowly lost the medal to Sweden's Jimmy Lidberg, with a three-set technical score (2–0, 0–1, 1–4), and a classification point score of 1–3.