Playing as a youth within the Swedish and Slovakian junior leagues, Dvorský as a part of AIK, opted to join HC '05 Banská Bystrica of the Slovak Extraliga for the remainder of the 2020–21 on 6 January 2021, making his professional debut as a 15 year-old.
[2] Dvorský returned to AIK for the 2021–22 season and was later signed to his first senior team contract, agreeing to a two-year deal, on 7 February 2022.
He opted to move to North American to play with Sudbury Wolves in the Ontario Hockey League (OHL).
[8] The postseason ended in disappointment after the Wolves were swept in the second round by the North Bay Battalion, but he nonetheless called his time in Sudbury "amazing".
[5] Dvorský won a gold medal with Team Slovakia at the 2022 World U18 Division IA Championships, scoring 11 points in only five games.