I daresay most people on this forum grew up playing videogames as children of parents who did not.
I'm very grateful to my parents because they always bought me and my brother the latest games and systems--starting with the NES all the way through the PS2, Gamecube, and Xbox--although they had mixed feelings about us spending a lot of time playing them. They wanted us to have a well-rounded childhood that included plenty of physical activity and creative pursuits. They were awesome parents in that regard.
The only other major restriction placed on us was based on ratings--I couldn't play "Teen" rated games until I was actually a teen, and I couldn't play "Mature" rated ones (with the exception of Halo) until I was sixteen.
That being said, I still spent way too much time playing certain games during my teenage years, including Star Ocean: The Second Story (PS1) and Phantasy Star Online (Gamecube).
Back then, they generally avoided actually playing games with me and my brother, probably because they were convinced that they'd suck at them. Lately, though, my parents have been enjoying Kinect Sports (they get a real kick out of the "highlight" reels at the end of each round) and Left 4 Dead. I'm probably going to try to get my dad into The Walking Dead since he loves the show.
Nope, mine do not understand video games in any way as they have zero interest in them, my mother was a bit strict about game ratings(I.E. she wouldn't let me get Soul Calibur on the Dreamcast, thankfully my cousin got me the game for Christmas) for a bit but she eventually loosed up.
I was pretty busy as a kid with several outside of school activities(most of which my parents forced me to join, like Boy Scouts which I despised), so ironically I actually have more time to play games now as an adult then I did as a kid.
The only issue my parents had was gaming for long periods, which could be a pain when some of the later 128k games could take 20+ minutes to load ! But it was normally ok as I was a sporty sort and was out more than I was in.
My father likes really simple straightforward shooters he always had a go on Phoenix in the arcades, 1942 was his favourite Spectrum game and his all time favourite is House of the Dead on Saturn with the light gun.
I have tried to introduce him to slightly more complex games but anything with more than one button gets short shrift.