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You don't need those on the games table.

GameTagID INT UNSIGNED,
GamePlatformID INT UNSIGNED,

Also, for the intermediary tables, you could use a composite primary key using both foreign keys.

CREATE TABLE GameTag
(
    GameID BIGINT UNSIGNED,
    TagID INT UNSIGNED,
    PRIMARY KEY (GameID, TagID),
    FOREIGN KEY (GameID) REFERENCES Game(GameID),
    FOREIGN KEY (TagID) REFERENCES Tag(TagID)
);

CREATE TABLE GamePlatform
(
    GameID BIGINT UNSIGNED,
    PlatformID INT UNSIGNED,
    PRIMARY KEY (GameID, PlatformID),
    FOREIGN KEY (GameID) REFERENCES Game(GameID),
    FOREIGN KEY (PlatformID) REFERENCES Platform(PlatformID)
);