This contentious relationship you state implies a fixed pie economy in which a person can get rich only at the sake of his fellows. Any thinking person would roundly reject such a notion.
You are technically correct. There is no finite pie. But there is a finite pie in our minds.
We behave instinctively as if there is a finite pie. We push our boots in others' faces instinctively, try to keep them down, shut them out, push them away, because our genes think the pie is finite.
Social networks do act so as to keep outsiders down. Not because it's rational, but they do.
On a similar topic is an essay by Paul Graham that you may enjoy: http://www.paulgraham.com/gap.html