Well, kind of yes, that depends what you means by saying "rich".

It's just that the whole system based on money is done/money is of no value anymore if AI takes ~95% jobs.

So what "being rich" becomes redefined, and that comes with a lots of various consequences.

It would basically mean "robot battles" over the land and technology, resulting in the annihilation of most of the mankind, if no proper regulations are introduced by the government.

And I'd suppose it might be in the best interest of the rich/government to introduce regulations that stops them from killing each other, which is basically how the world is set up right now (at least to a certain degree, as no system is perfect).

AI is already responsible for dealing with around ~85% (don't remember the exact number) customer support - the "human interaction" kind of job.

AI isn't replacing doctors or lawyers anytime soon, but let's be honest, AI is going to be much better at diagnosing than real doctors pretty soon. But that will just result in improved quality of healthcare, as I'd expected the doctor will have to approve AI results.

Anyway, there's really no way to predict how AI is going to impact the world.

It's most likely to take ~95% of current jobs, but If that happens and no new jobs are created and no proper regulations are introduced, then there's no "being rich" anymore, as in such scenario the whole economy just collapses. It's not about who has more money anymore, it's about who controls the AI. So it might be in the best interest of the billionaires to introduce certain regulations, resulting in a "good" outcome for all humankind.

"Good" scenario might result in free housing, guaranteed income, and overall well-being for everyone.

No one knows which way things are going to develop.