Nowadays you can have the 50 year old dad spending his quality time in bed next to his wife blasting enemies with the teenage/student kids doing the same.
With another generation it will be the folks in retirement homes too.
With music you get stuck on the stuff you discovered and made your own. Into punk? Probably born way back in the 60s. Techno? 70s.
Will it be the same with games? The guy in the retirement home still playing World of Warcraft? Or that copy of Diablo that came out in 2003?
Story in video games therefore has to be good enough to not just last a week or a summer, but a lifetime.