How will the Repubmocrats keep 100% power against independents, tea party and other radical despots competing against the chosen ones?
It's called 'First Past the Post', and Facebook has nothing to do with it.
You're right that "first past the post" is a big part of the problem. But that's far from the whole story.
For one thing, "Repubmocrats" do NOT have 100% of the power. It may be near 100%, but it isn't 100% -- for example currently two U.S. senators, four major city mayors, and hundreds of state and local officials across the U.S. are elected independents or members of 3rd parties.
That means that quite a few voters across the U.S. have actual experience in ELECTING someone who is not a member of the two major parties. Those sorts of successes can make it more easier for some voters to justify taking a chance on a 3rd-party candidate.
Also, the Tea Party (for another example) has made huge inroads into mostly Republican territory in recent elections. One can argue that this has created huge problems for the traditional Republican leadership that disagrees with Tea Party ideology. In some elections, this has resulted in long-standing prominent members of the Republican party losing primaries and/or general elections.
The video you posted labels this the "spoiler effect" when it leads to, say, a Democrat being elected. But the very term "spoiler effect" is not a neutral term -- it's a propaganda term used by the 2 major parties to convince people to keep them in power.
We could, instead, call this the "disenfranchisement effect," where the two-party system focus on candidates A and B might disenfranchise voters who hate both and would prefer to vote for C. According to the spoiler effect logic (and your video), the C voters supposedly should learn between elections that their votes were "wasted" by voting for C, and thus come back and vote for A or B in the next election.
But that's not the only choice the C voters have. They could also (1) not vote at all, because they believe they've been effectively disenfranchised by the two parties or (2) continue to vote for a candidate like C, as the only candidate who represents their views. (One could certainly argue that at least condition (1) is incredibly important in the U.S. today, given the "get out the vote" efforts both parties employ, and also the fact that most adults don't even bother to vote in most U.S. elections.)
The point of all this is that while "first past the post" gives a mathematical tendency toward two party domination, it does NOT guarantee that the two parties will always stay the same -- one could eventually be replaced by another, or (more often) one or both parties could shift ideological ground significantly to retain members in the face of increasing defections in major elections.
This in fact has happened many places with the Republicans for example, where Tea Party affiliates have forced the Republican party candidates to change their ideologies or else lose elections. Rather than seeing it as a "spoiler" effect to lose an election, many voters instead see it as effective "disenfranchisement" and refuse to continue voting for candidates they hate. The only choice of the Republicans is to nominate candidates that have a chance of winning... and thus, to retain power, they must actually respond to those voters who cast votes for 3rd parties (or didn't even vote at all).
So, it's not quite as dire as people make it out to be. Yes, "first past the post" sets up some unhelpful constraints, but significant change is still possible. We can start by refusing to use 2-party propaganda terms like "spoiler effect," since that implies that one of the top two candidates somehow "deserves" to win. Untrue. If a 3rd-party candidate draws enough votes away from one of the top 2 candidates, the major party candidate FAILED to attract enough votes to win. That's not a 3rd-party candidate "spoiling" an election -- that's a major party "losing" an election by failing to satisfy enough of the electorate.