What the study shows is that a tiny minority of the population happens to pretty much always get what they want politically even when the majority of the population disagrees. This necessarily implies that the minority is able to manipulate the system in a way beneficial to them as the study explains in great detail. Manipulation of the vote through the means described in the video is a core part of this.
You seem to be confusing the mechanics of how capitalism works where wealth accumulates with a handful of people with the process of democracy. The wealth accumulation itself isn’t what’s influencing the democratic process. The influence is expressed via ownership of the media, funding of politicians, lobbying, guiding policy decisions, and so on. These are the tangible actions the oligarchs take to mold the system to their interests.