One victory by Kirk occurs when Spock is distracted by a danger to the ship that Kirk is not concerned about.

In "Where No Man Has Gone Before" Spock is one move from checkmating Kirk when they are interrupted. In this case, Kirk is concerned about a mysterious distress signal.

In "Charlie X" Spock loses unexpectedly (as you say, not even aware that he is in danger of checkmate). In this case, Spock is the one who is distracted - just before the checkmate, Spock is perturbed by Charlie's mysterious knowledge of the fate of the Antares before the Enterprise's sensors detected a problem ("He seemed to know what happened to the Antares before we did."). Spock is not entirely emotionless, no matter what he says, and a possible danger to the ship is more important than chess.

The other episodes that feature 3-D chess don't feature Kirk and Spock playing each other (unless I'm missing one).

We don't have much evidence about how often Kirk wins. In the two games shown on screen, one ends before the game is resolved, and Spock loses the other (with extenuating circumstances).

In "Where No Man Has Gone Before" Spock says he is one move from checkmating Kirk, but Kirk finds a response that does not immediately led to him losing (the game is then interrupted so we don't see whether Spock or Kirk would have eventually won the game). This is possibly an embarrassing mistake on Spock's part, but it could be interpreted as a simple fact equivalent to Spock saying "There is a possible next move for me that wins the game," and Kirk then making a move that eliminates that possibility.

In "Charlie X" Spock loses unexpectedly (as you say, not even aware that he is in danger of checkmate). In this case, however, Spock is distracted - just before the checkmate, Spock is perturbed by Charlie's mysterious knowledge of the fate of the Antares before the Enterprise's sensors detected a problem ("He seemed to know what happened to the Antares before we did."). Spock is not entirely emotionless, no matter what he says, and a possible danger to the ship is more important than chess.

The other episodes that feature 3-D chess don't feature Kirk and Spock playing each other (unless I'm missing one).

One victory by Kirk occurs when Spock is distracted by a danger to the ship, that Kirk is not concerned about.

In "Where No Man Has Gone Before" Spock is one move from checkmating Kirk when they are interrupted. In this case, Kirk is concerned about a mysterious distress signal.

In "Charlie X" Spock loses unexpectedly (as you say, not even aware that he is in danger of checkmate). In this case, Spock is the one who is distracted - just before the checkmate, Spock is perturbed by Charlie's mysterious knowledge of the fate of the Antares before the Enterprise's sensors detected a problem ("He seemed to know what happened to the Antares before we did."). Spock is not entirely emotionless, no matter what he says, and a possible danger to the ship is more important than chess.

The other episodes that feature 3-D chess don't feature Kirk and Spock playing each other (unless I'm missing one).

One victory by Kirk occurs when Spock is distracted by a danger to the ship that Kirk is not concerned about.

In "Where No Man Has Gone Before" Spock is one move from checkmating Kirk when they are interrupted. In this case, Kirk is concerned about a mysterious distress signal.

In "Charlie X" Spock loses unexpectedly (as you say, not even aware that he is in danger of checkmate). In this case, Spock is the one who is distracted - just before the checkmate, Spock is perturbed by Charlie's mysterious knowledge of the fate of the Antares before the Enterprise's sensors detected a problem ("He seemed to know what happened to the Antares before we did."). Spock is not entirely emotionless, no matter what he says, and a possible danger to the ship is more important than chess.

The other episodes that feature 3-D chess don't feature Kirk and Spock playing each other (unless I'm missing one).