CervelloYM: Back in my day, we could play any game we wanted without our parents poking their noses in. We were the masters of our own gaming destiny! No helicopter parents telling us what to play or what was "appropriate."
My big sister tried, but luckily no one listened.
I was even able to see RoboCop and later Cyborg uncut in the cinema being only 10 years old. The cinema owner didn't care either :D
Back in these days explicit violence was a lot less visible in games anyway. It was still a long way to Mortal Kombat.
And I can't really remember any story based games for kids from the years to come, it was all just platformers, fighting games, brawlers, Shoot'Em'Ups and racing games. Graphical adventures for kids only really started in the early to mid ninetees.