I have a very high IQ (99.97% percentile) and I agree there's a difference between intelligence and cultural knowledge.
In my case, my parents read a lot to me, and as soon as I learnt how to read myself I would devour books.
I was raised trilingual, though not on purpose (my parents' language + 2 co-official local languages), and got started on my 4th language by the age of 5. There is scientific evidence that learning multiple languages from an early age is extremely beneficial to the brain.
We didn't have game consoles or a laptop, and I'm early 20s so they were definitely around. Family PC was purchased in 2010, by which point I was about to start secondary school, so had no exposure to screens throughout my childhood.
If you were bored, you were encouraged to find a new book, play with your siblings, clean something, or go to the library to work on some imaginary project. It wasn't my parents' job to entertain us. One summer I learnt the Greek and Hebrew alphabets out of boredom. I spent weeks writing my journal in Greek or Hebrew characters, or came up with an entire fake system.
My parents are both working class, very low-income people, but they tried to expose us to as many activities and topics as possible. Museums, zoos and farms... Big exposure to the arts, which challenges the artistic and creative sides of the brain (music in my case, which was thankfully free and state-subsidised in my home country).
We were always spoken to like adults, so from an early age we would discuss the evening news, current events, sports... Family finances were discussed openly at the dinner table.
We used to take a road trip every summer across Europe to visit my grandparents, and from the age of 6-7 we could confidently read maps and figure out a route through X country on our own. My mum would teach us the correct pronunciation of each language of the countries we were passing through, she read up on the basic rules of each one of them.
We didn't go to private school so the exposure to sports and social networking wasn't there. I'm actually quite inept when it comes to middle/upper-class social events. I don't know how to dress or what the table etiquette is.
I'm not an avid public speaker but we went to church every week and were always involved in the children's programmes, choir concerts, then did readings when we got older. That gave us confidence.
I got into university at 15 and moved abroad a few months later, after finishing school 2.5 years earlier than normal. Now as a young adult, I try and expose myself to everything we didn't have access to as kids, because like I said earlier intelligence and cultural knowledge are two different things. I definitely still lack in the latter!