The truly interesting question, and the crux of the matter, also hasn't changed much since 1903:
How?
It did absolutely change, a lot, it was one of the main themes of the 20th century: revolution. In the old sense of the word, turning the social order upside down.
It took many forms: capitalist social democracy, communism, fascism, feminism... Left or right, without making a value judgement, they were all revolutions seeking to empower the working masses.
Of course, when you get rid of kings, it's really really hard to make sure the vacuum is not filled by something even worse. Credit where credit's due, as a European, I do believe that the US is one of the few cases that was somewhat successful in not completely bungling this opportunity (although there's the detail of slave labour, and the conquest of natives...).
And after many-many horribly failed attempts, much of the world did end up in a relatively healthy state around the second half of the 20th century. Fukuyama's end of history and all.
Now we seem to be regressing again. Perhaps it's part of the eternal cycle and it was always coming. Perhaps it's not actually regressing all that much, and it just looks like it to our coddled selves, or we have become more ambitious on what we think is right. Perhaps people have found new loopholes (tech) on how to get ahead and dominate the rest of us, and we just need to catch up and get it under control again.
Perhaps that quote from 1903 is relevant now, but it doesn't mean that it was relevant the whole time since. Perhaps it was, I wasn't there.
Revolution!
There's been plenty of examples of workers seizing the means of production and establishing sustained non-capitalist organization (State or otherwise). We have any number of strategies to choose from: The PRC, Soviet Union, Syndicalized Spain (my favorite, seems the least likely to lead to police state), Vietnam, Cuba. The question thus isn't "how," but more specifically a couple other questions: "How do we prevent capitalist forces from liberalizing our movement (PRC, Soviet Union)," "How do we prevent fascists from killing us all (Syndicalized Spain)," "How do we prevent becoming a state-capitalist police state that halts the revolution (PRC, Soviet Union)"?
If you ignore everything that happened in between 1903 and today, it might seem like we've never made any progress on this, but at least in the US wealth inequality was demonstrably not as much as an issue for some of the time in between. For a time in the 20th century, it was possible for someone solidly middle class in the US to be able to save up a bit of money and afford a down payment on a house within a decade of working. That's something we've lost to time now, and it's not because it's impossible to achieve or because of the bogeymen of DEI making the fruits of labor and technology too sparse to share with everyone, but because an increasingly large portion of the pie is going to an increasingly smaller set of people.
The delta between 1903 and today in this regard might be small, but the line between them isn't flat, and that makes it even more tragic and frustrating to have this questioned as if it's an impossible problem.