>Wealth, while not an exclusive means to power, can buy you power in more ways than one.
Wealth only buys you power if people are willing to accept your money, and are also refraining from simply using force to take your money from you.
>Look at corporations making the game without firing one gun.
That's because they have an entire government, with guns, enforcing the rules of the game they're playing. If the government suddenly decides to confiscate all their wealth, there's absolutely nothing they can do about it. This has happened multiple times in history (such as the Cuban Revolution).
>And a few examples of rebellions or revolutions where people have overthrown the rich just show poor management on the side of the rich.
No, it shows that at some point, having money doesn't overrule people willing to use violence against you. Most of the time, this is avoided because people tend to prefer to avoid violence, and because there's enough people willing to defend the status quo (where that money is valued), but sometimes that breaks down, and then no amount of money will save you.
It's very simple: a handful of wealthy people can never be a match for an army of people with guns. The only reason wealthy people have any kind of power is because there's an army behind them backing their claim to power.