Can someone please help me understand why people like this author claim that capitalism uniquely requires economic growth.

When the entirety of an economy must be funded with borrowed money the only way the math works is for GDP growth to cover the cost of borrowing. This is the result of neoliberalism, not capitalism as most people picture it.

When most people think of capitalism they envision the "mom and pop" business owners who are the real driving force of our economy. They don't see the bankers and fund managers that use money creation to gain their profits, or their central government as the only entity that can create money without the demand and overhead of interest.

To protect the laisse faire system that enables the "real" profit of capitalism the people need to be ignorant of how their money works and how it is created. This is the purpose of the fear porn surrounding our federal finance system that most people are convinced is driven by taxation, presenting a "cost" and higher overhead.

The reality is that taxation (and bonds) cannot "fund" anything at the federal level because one cannot collect or borrow what doesn't yet exist, and only the federal government can create the money necessary to pay taxes or loan back to Treasury. This "new" money creation is also the only way that private sector debt can be "net" retired without rolling it over into new debt via a constant increase in GDP.

There is no "national debt" that taxpayers are responsible for repaying. It is nothing more than an accounting of the net money supply, dollars that have been created by Congress and not yet used to pay a federal tax obligation.