Oh, I see what you're saying. You mean that wealthy individuals will someday be able to use technology to completely automate out the need for goods and services from others. That seems farfetched, even in a mostly automated economy. Somebody's still got to produce, upgrade, and repair all those bots. Not to mention greet people on the phone, give haircuts, make sales, and do other jobs that benefit from a human touch.
Now if those bots can produce, upgrade, and repair themselves, and do jobs in a "human" way, that's approaching strong AI. At that point if everything is automated top to bottom from mining raw materials to a finished product, why wouldn't it all be free for everyone? That sounds like a post-scarcity economy to me, so it would seem pointless to hoard at that point. Backing up, the reason why I disagree with you and the video is because I think that over the long term, the more things get automated, the cheaper they'll be, for everyone, and therefore overall everyone's real wealth has gone up, on average.
It is easy to say that this may result in a greater concentration of wealth, and that will probably be the case. Where I disagree is that it will result in the "everyone else" group being worse off than they are now. At the very least I think their/our quality of life would remain the same. I don't think overall wealth will increase slower than the concentration of wealth, if that makes sense.