“The analysis by economists from the Office of Management and Budget and the White House Council of Economic Advisers drew from publicly available data and says the disparity is driven largely by how the tax code treats income generated from wealth — such as income from stocks, whose worth increases over time — rather than wages, which are immediately taxed.”

It looks again that they are talking about estimated increases in asset values and trying to represent that as income. It is only income if it is sold.
Will the government ever get its hands on money from the increase in value if the owner never sells it (and therefore doesn’t have a personal benefit from the increase in value)? Yes. Upon death they can apply an inheritance tax to the value of the asset,