Born in Kiselevsk in the former Soviet Union, Dolmatov's solid yet enterprising style of play was soon to launch him to the forefront of youth chess, culminating in him winning the World Junior Chess Championship in 1978.

Along with the titles, the early part of his chess career yielded many international tournament victories, including the Amsterdam Masters 1979, Bucharest 1981, Hradec Kralove 1981, Frunze 1983, Barcelona 1983, as well as the traditional closed Tallinn (Keres Memorial) 1985 and Sochi (Chigorin Memorial) 1988.

Despite winning at Hastings (1989–90, then still a major round-robin tournament) as clear first and qualifying as a World Championship candidate from the strong Manila Interzonal of 1990, Dolmatov narrowly failed to convert his 'preliminary round' match against his friend Artur Yusupov the following year.

Nevertheless, during this period his Elo rating exceeded 2600 and he managed to maintain this level for the next decade.

There was some success in the latter part of his 'busy' period, notably the Linares Open of 2000, but at the Moscow Aeroflot Open of 2004, Dolmatov famously lost a game to 13-year-old Magnus Carlsen in just 19 moves.