Abolishing private property, what you suggested in the context of consumers of Amazon vs mom and pop stores, is 100% communist.
Opposing monopolies is neither communist or capitalist. Free market price theory does not suggest that monopolies are good for anyone except the monopolists. In the USA, the railroads were the early textbook example. Monopolies are NOT free markets with or without the law opposing them. Monopolies, like communism, are in direct opposition to free markets.
I don't believe the super rich like Bezos, Buffet and Bloomberg put idealogy over the value of coin. They'll get richer any way they can, whether through communism, capitalism, monopolies or taxes and regulation. You put it all together with corrupt powers at the top, and you have crony capitalism... what we see in one form or another in varying degrees in Russia, China, the EU, South America and the USA.
This is why I try to avoid left vs right, capitalism vs communism, debates. But, abolishing private property... that's communism.