We can also look to Troi beating Data at 3D chess: (note: 3D, not 4D)
(a 3D chess game is in progress)
DATA: The characteristic response to the Kriskov Gambit is to counter with the el-Mitra Exchange, particularly since I have already taken both your rooks. By missing that opportunity, you have left your king vulnerable.
TROI: We'll see.
DATA: As you wish, Counsellor. Check.
(Troi makes her move)
DATA: Intriguing. You have devised a completely unanticipated response to a classic attack. You will checkmate my king in seven moves.
TROI: Data, chess isn't just a game of ploys and gambits. It's a game of intuition.
DATA: You are a challenging opponent, Counsellor.
If Troi can beat Data (who is likely arguably an even better strategist / calculator than Spock), Kirk, who Spock says used similar unexpected tactics and unpredictable reactions, also stands a good chance.
Also - in the game we see Kirk and Spock playing - Kirk is very much aware of Spock's half-human side and is goading him, which could cause Spock to make a blunder:
KIRK: Certain you don't know what irritation is?
SPOCK: The fact that one of my ancestors married a human female
KIRK: Terrible having bad blood like that.
(later, to Mitchell)
SPOCK: He played most illogically. His next move should have been the rook.
Spock's response to Gary Mitchell as to the chess game clearly shows that Kirk, like Troi, played illogically, which created the win condition. Spock's insistence that Kirk should have played a particular move, indicates a bit of unwillingness to adapt to simply 'play the board' as Jeremy Silman (chess player / author) suggests.
(Similar to Data vs Kolrami in a game of Strategma, where Data plays not to win, but simply not to lose, which is an unexpected and maddening tactic to his opponent)