As near as I can tell, their logic is basically:

1. Imagine AI replaces all jobs.

2. Since AI is controlled by a very small number of people, they will be the ones that get all the money, since they are doing all the work.

3. Since there are no jobs, everyone else will die because they won't have money to buy anything.

But this causal chain makes no sense.

Imagine that I find a Magic Lamp that grants me unlimited wishes. Suddenly, I don't have to work! I wish for a sandwich, I get a sandwich. I wish for a car, I get a car. Etc.

Does the economy collapse? Of course not, because everyone else still has to work for a living (the poor fools). The fact that I don't need a job has effectively removed me from the economy.

One day I discover that I can wish for another Magic Lamp! I give the new Magic Lamp to another family and now they remove themselves from the economy. After a few weeks, 10,000 people have their own Magic Lamp. Has the economy collapsed? No, because the remaining 8 billion people still form a robust economy.

In this scenario, the economy won't suffer until a significant percent--maybe 50% or maybe 90%--have Magic Lamps. But at that point, it's no longer controlled by a "small number of people."

One argument is that once I have a Magic Lamp, I can disrupt the economy by (e.g.) creating cars for free and selling them for cheap. There's no incentive for me to do this--I don't need money--but let's pretend I'm doing it just to help people. Now a lot of people have cars but also a lot of car builders are out of a job. That sucks.

But wait! More cars also means more jobs. If you don't have to pay for a car, then you can use the money to pay for a driver. You have more cars, so you're paying more for insurance, so now there are more insurance jobs. There are more accidents, which sadly require more hospitals. And we need to hire people to dispose of all these cars at end-of-life.

If I use the Magic Lamp to get rid of part of the economy, the other parts get bigger because (a) there is more money to spend on it, and (b) there is often more need.[1]

The only way I can really destroy the economy with a Magic Lamp is to give everyone a Magic Lamp. But that's not a dystopia--that would be paradise!

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[1] If you don't believe this, just consider farming. Farming used to be 90% of the economy. Now the revenue from farming is concentrated in less than 5% of the people of the US. Did everyone else starve? Are we all out of jobs? No--the rest of the economy grew.