Is that the kind of gun you buy?
Saying power gives you power is a circular argument. Wealth is like a wildcard, it can be turned into anything. And it's greatly amplified by experience as a guide to turning it into power, and allies by your side.
With wealth you buy the tools needed to stay in power: guns, lobbying, policy making, political campaigning, influencing public opinion or education, etc. No wealth and allies, no tools. Look at corporations making the game without firing one shot.
The entirety of human history showed that wealth has always been able to buy power better than anything else. And a few examples of rebellions or revolutions where people successfully overthrew the rich just show poor management on the side of the rich. Plenty more have died with guns in hand. Guns given to them by someone wealthy.
Later edit: I have edited the comment a bit for clarity, I noticed the reply later.