Kunin was born on September 28, 1983 in Saratov, Russia. When he was 10 years old, his family moved to Germany where he began to receive a significant chess education. He became a student of Grandmaster Aleksandar Miladinović and began to compete regularly for the chess club in Tübingen.
Kunin's competitive achievements include becoming the champion of the State of Baden–Württemberg in 2003, 2006 and 2007, and the Challenge Champion of Evry in 2006. He also contributed to Germany's second-place team finish in the 2005 European Team Chess Championship.
Now based in Tübingen, Germany, Kunin plays regularly for the Chess Friends of Tübingen in the Oberliga Baden-Württemberg, and the Chess Club of Deizisau in the German Chess Bundesliga. He also played in the French Top 16 league in 2008 for the club of Vandoeuvre.