Drozdovskij's most notable accomplishments in his chess career include his victory in the 2001 Ukrainian Championship, his win in the 2003 European Championship, and his triumph in the 2004 World Chess Championship in Tripoli, reaching the third round. He has also played for the Ukrainian team in the 2005 World Team Chess Championship, 2013 European Team Chess Championship and several Chess Olympiads.
In 2001, at age 16, he was awarded the International Master title, and two years later at 19 years old, he earned his Grandmaster title. Drozdovskij has stated that he is proud of being one of the youngest participants to have achieved the grandmaster ranking.
Beyond his accomplishments in conventional chess, Drozdovskij has experienced success in online correspondence chess. He won the ICCF World Cup 18 and the 30th ICCF World Championship, making him the Correspondence Chess World Champion.