In 1922, Richter for the first time won the Berlin City Chess Championship. In 1928, he tied for 1st–2nd in Berlin. In 1928, he won in Wiesbaden. In 1930, he tied for 4–5th in Swinemünde. In 1930, he tied for 3rd–5th in Prague. In 1931, he lost a match to Gösta Stoltz in Berlin. In 1931, he took 2nd, behind Ludwig Rellstab, in Berlin. He played for Germany at two official and one unofficial Chess Olympiads: at fourth board at Hamburg 1930, fourth board at Prague 1931, first board at Munich 1936. He won two team bronze medals and one individual bronze medal. In 1932, he won in Hamburg. In 1932, he tied for 1st–2nd in Kiel. In 1932, he took 3rd in Berlin. In 1932, he took 4th in Swinemünde. In 1932/33, he tied for 1st–2nd in Berlin. In 1933, he took 2nd, behind Efim Bogoljubow, in Bad Aachen. In 1933, he tied for 5–6th in Swinemünde. In 1933, he tied for 4–5th in Bad Salzbrunn. In 1934, he took 2nd, behind Gideon Ståhlberg, in Bad Niendorf. In 1935, he tied for 1st–2nd in Berlin. In 1935, he took 2nd in Swinemünde. In July 1935, he won in Bad Aachen. In September 1935, he played in Zoppot. In 1936, he won in the Berlin championship. In 1936, he took 2nd in Swinemünde. In 1936, he tied for 8–9th in Poděbrady. In 1937, he tied for 2nd–3rd in Berlin. In 1937, he took 4th in Bad Elster. In 1937, he tied for 1st–2nd in Bad Saarow. In July 1937, he took 2nd, behind Georg Kieninger, in Bad Oeynhausen. In 1937, he took 3rd in Berlin. In 1938, he took 9th in Bad Harzburg. In 1938, he won in the Berlin championship. In 1938, he tied for 4–5th in Berlin. In July 1938, he tied for 5–7th in Bad Oeynhausen. The event was won by Erich Eliskases. In May 1939, he took 2nd, behind Bogoljubow, in Stuttgart. During World War II, Richter played in several strong tournaments. In June 1940, he won in Berlin, and took 2nd, behind Bogoljubow, in Berlin. In August 1940, he tied for 3rd–4th in Bad Oeynhausen. In November 1940, he took 3rd in Cracow/Krynica/Warsaw. In 1941, he tied for 3rd–4th in Berlin. In August 1941, he took 3rd, behind Paul Felix Schmidt and Klaus Junge, in Bad Oeynhausen. In September 1941, he tied for 5–6th in Munich. The event was won by Stoltz. In September 1942, he tied for 3rd–5th in Munich. The event was won by Alexander Alekhine. After the war, he participated in the Berlin championships. He tied for 1st–2nd, tied for 3rd–4th, tied for 2nd–3rd, took 2nd, took 3rd. Awarded the IM title in 1950. He was co-editor of Deutsche Schachblätter and Deutsche Schachzeitung. Author of several chess books.
The Richter–Rauzer Variation of the Sicilian Defence occurs after 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 Nc6 6.Bg5. The Richter–Rauzer Variation was named in honor of Kurt Richter and the Soviet master Vsevolod Rauzer. The Richter–Veresov Attack was also named after Kurt Richter and Gavriil Veresov. It most commonly occurs after 1.d4 d5 2.Nc3 Nf6 3.Bg5.
