Who Wins the Knight’s Game? A Game Theory Challenge!

\color{orange}{\text{Dominik}} and \color{cyan}{\text{Smbat}} play a game on an \color{red}{\text{8}} \color{red}{\times} \color{red}{\text{8}} chessboard.
\color{orange}{\text{Dominik}} starts by placing a \color{red}{\text{knight}} on one of the squares.
Then the two players, starting with \color{cyan}{\text{Smbat}}, alternately move the \color{red}{\text{knight}} according to standard chess rules.
No square may be visited more than once, including the initial square.
The game ends when a player cannot move; that player loses.
Who has a winning strategy and why?

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