Depends on the type of game. Some are entirely story based.
Early games, there was no back story, no plot. Just 'go'.
Asteroids, Space Invaders, nearly any arcade game. Not until Donkey Kong did they even implement a extremely basic premise in the game, and by basic I mean 'monkey steals girl - rescue girl'.
Then came Dragon's Lair. You tried to play a story. RPG's took off around then.
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I agree.