The game isn't rigged because it isn't zero sum. Billionaires getting richer doesn't normally impact your ability to get richer. And as long as you're free to maneuver how you'd like, it shouldn't really matter to you that someone else is succeeding faster or slower.
Also, it's generally the case that there are more opportunities to turn $1 into $2 than to turn $1B into $2B.
> Billionaires getting richer doesn't normally impact your ability to get richer.
I believe this is not true for multiple reasons.
First - regulatory capture. Once a sector of economy generates a handful of billionaires, legal / regulatory barriers go up which make it much harder for startups to compete.
Second - competitive barriers. Google can acquire all the search channels (eg. paying Apple and Mozilla billions of $$$ to be the default search engine on iOS / Firefox).
Third - price undercutting by subsidizing a subset of the incumbent's product portfolio by profits from other parts of the business. See: Amazon vs diapers.com.
So yes, the game is definitely rigged in favor of billionaires.
What makes MLM schemes bad is not that the people at the top make money faster, but that people who aren't on the top tend to not make any money at all. This is a direct result of the fact that many MLM schemes are actually pyramid recruiting schemes, where you profit primarily by recruiting people beneath you. If everyone is doing this, then recruiting grows exponentially, and it doesn't require many levels before you run out of people to recruit, which prevents anyone below the top levels from making significant money.
Obviously capitalism doesn't have that problem, since it's driven by the sale of goods and services, not by one-time recruiting commissions that we'll some day exhaust.
TL;DR — Your analogy doesn't hold, as the market is not a fixed pie zero-sum game.
Also, it's generally the case that there are more opportunities to turn $1 into $2 than to turn $1B into $2B.