Yes, probably.
gameId INT
player1Id INT
player2Id INT
gameEnded DATETIME NULL
gameNotation TEXT
I would likely break it out to:
Games:
id INT NOT NULL <-PK,AUTOINCREMENT
white_player_id INT NOT NULL
black_player_id INT NOT NULL
gameEnded DATETIME
Moves:
id INT NOT NULL <-PK,AUTOINCREMENT
game_id INT NOT NULL
move VARCHAR(9) NOT NULL //Change length if necessary