"Game pressure" to me connotes a specific type of pressure though -- that brought about by the confluence of time in the game, and the score. The pressure of getting a shot off at the end of a shot clock in the first half or the pressure to not let your teammates down, while forms of pressure, are not "game pressure" in that context.
So I don't see it as redundant; I see it as specifying a specific subset for the sake of being particular.