The expression “Keeping up with the Joneses” was popularized in a newspaper comic strip from 1913, and today is a disapproving way to say that someone is trying to match someone else in conspicuous consumption.
It would be appropriate if, say, all the billionaires were all competing to build their own spaceships, even bigger and flashier than Elon Musk’s, and then Elon Musk announced he was selling SpaceX and donating the money to public health in Africa. Or if Mark Zuckerberg had the most incredible backgrounds on his Zoom meetings, or the fanciest costumes, and everyone were trying to outdo him, and then he just started turning his camera off so they could focus on getting work done.
That’s not what’s happened here, though: the irony is that Zuckerberg wants privacy for no one but himself. I like the suggestion of, “Do as Zuck says, not as he does.” Or maybe, “Zuck’s built a glass house, for us, and now he’s throwing stones.” Or just something sarcastic about how much Zuck values privacy.
There’s also, as others have mentioned, a grammatical error in the sentence. If we were talking about the scenario where the billionaire who started the competition has bowed out of it, I might say something like, “and Mr. Jones has just gone off to live in a cave,” or “but Mr. Jones has moved into a cave with a goatskin and some sticks.” Either of those gets across that Jones used to show off, but has stopped.