While the internet was probably a good source of information I'd play it down to mentorship as the decisive factor. In all of these cases, the successful teenagers seem to be lucky enough to either have a good private mentor, be enrolled in a mentorship program, or be enrolled in a highschool famous for the encouragement and resources that it provides to it's enterprising students.
In contrast many of us would have been told to "aim for a simpler project" if we proposed something like that to our computer science teachers.
Your post summarizes Malcolm Gladwell's book Outliers on extremely successful people quite well -
it's mostly being born to a) rich parents who can afford to pay for extra-curricular activity, good schools or who have the time to "improve" their kids or b) being around schools or universities that can recognise the talent and give talented kids the input and resources they need. Both a) and b) are based on pure luck.
Rich parents, exclusive school (with their own computer! unheard of at the time) and local companies that let Gates and other kids screw around on their computers. Luck!
I both agree and disagree with your post. I do agree that people's discoveries and successes are very much based on luck (i.e. external factors), but I don't think personal accomplishment, progression, and overall contribution is luck based. Sure, becoming a Mark Zuckerberg takes luck, but the only difference between him and other people (assuming sufficient time in a certain subject) is that the general public liked and found a use for Zuckerberg's idea more. Essentially, success is luck-based, but genius is not.
I do think that without hard work/talent Bill Gates and all these other successful people wouldn't be where they are now, but without luck and the correct circumstances all the hard work in the world doesn't bring you anywhere, your genius won't help you.
Look at William S. Burroughs' life - an extremely talented writer from a rich family, who still "dropped out of society", later befriended Kerouac and Ginsberg who were the big factors (reasons?) in him becoming a great writer from age 40, without these people we wouldn't know the name; his genius wouldn't have helped him alone.
I don't like this term "genius", as there is no such thing. We need to move on from the idea of "being a genius", which is a modern phenomenon originating from then phrase to "have a genius", where genius is latin for genie. When we call someone a genius, we're saying that they are a mythical all-knowing being, which seems to absolve us from having to think about why a person is the way they are, and why we are not. It is the intellectual equivalent of burying our heads in the sand when we see someone brilliant, and ensures that we'll never really understand or appreciate success.
The term 'genius' bothers me too because it seems calling someone a genius is less about the object (ie the person we are talking about), but more about the speakers feelings toward that object (eg godlike awe etc).
In contrast many of us would have been told to "aim for a simpler project" if we proposed something like that to our computer science teachers.