Dorfman played in several USSR championships. In 1975, he took thirteenth in Yerevan (43rd URS-ch; Tigran Petrosian won). In 1976, he finished fifth in Moscow in the 44th Soviet championship as Anatoly Karpov won by a full point over Yuri Balashov.[1] One of his most emphatic victories occurred in qualification for this championship, at the 1976 First League tournament, where he finished 1½ points clear of the field (+6 =11). In 1977, he was joint USSR Champion with Boris Gulko (both +4 =11, ahead of Petrosian, Polugaevsky and Tal).[2] The subsequent play-off match was drawn (+1 –1 =4).[3] In 1978, Dorfman shared thirteenth in Tbilisi as Tal won.[4] In 1981, he tied for 8-9th in Frunze; Lev Psakhis and Garry Kasparov won). In 1984, he took 12th in Lvov (51st URS-ch; Andrei Sokolov won).
In international tournaments, Dorfman tied for second at Pécs 1976, finished second to Smyslov at São Paulo 1978,[5] tied for second at Polanica Zdrój 1978, one-half point behind Mikhail Tseitlin,[6] 1st-3rd at Djakarta 1979, 3rd-5th at Manila 1979. He won at Zamardi 1980. He was a winner at Warsaw 1983 (+6, =8), was 1st= at Lvov 1984, 1st at Moscow 1985, and 5th= at Minsk 1986.
In 1998, Dorfman won the French Chess Championship in Méribel (73rd FRA-ch).[7] Two years later, he was runner-up to his former student, Bacrot.
Dorfman was awarded the IM title in 1977 and the GM title in 1978.
Coach
He acted as one of Garry Kasparov's seconds in his first four World Championship matches against Anatoly Karpov. Later Dorfman moved to France. He coached the French player Étienne Bacrot from age nine to Grandmaster level, when he became France's and the world's youngest ever.
In 2004 Dorfman was awarded the title of FIDE Senior Trainer.
Commentator
In April 2019, Dorfman joined chess24 as one of the site's commentators and coaches together with Laurent Fressinet and Jean-Baptiste Mullon.[8]