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I agree it's not perfectly explained. But I think someone new to ergodic theory would find the article clearer (or at least more helpful overall) than your second paragraph here.

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“What we're seeing is that even though the expected value is positive, and the ensemble average is increasing, the time average for any single person is usually decreasing. The average of the entire "system" increases, but that doesn't mean that the average of a single unit is increasing.”

Someone new to ergodic theory may understand from that article that if wealth was ergodic the average for every trajectory would increase like the average for the entire system. But that doesn’t make sense.

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