You can't have wage labor unless you have money as a construct.
That sentence just clarifies what the first sentence implicitly requires, as you cannot trade for profit unless you have property rights, etc.
> Also during Pericles' tenure, pay for civic service was instituted. No single other reform furthered democracy as much as pay for service. Now many more people could afford to serve, and for some, serving became attractive financially. First, dicasts, or jurors, began to be paid. A low rate, but half a day's wages or so. That was introduced by Pericles while Cimon was still around, perhaps to counteract his liberality with his own wealth. Jurors were appointed by lot annually and could serve year after year. By 422 (Aristophanes Wasps 662), there were 6,000 jurors per year. Cleon increased the pay rate to 3 obols a day. Pericles also started the payment of soldiers and sailors 3 obols a day.
https://www.uvm.edu/~jbailly/courses/clas21/notes/atheniande....
You have a very formal, academic understanding of capitalism while we are arguing that the fundamental ideas of capitalism naturally exist because that's logical for human psychology - owning things, trading, markets, paying people for labor. This is all stuff that goes back to the earliest recorded records. Cuneiform tablets are just endless accounting ledgers.
It's economy wasn't modern free market system focused on capital accumulation and investment for profit. It was a mixed economy with significant state involvement and a variety of revenue sources that went beyond simple market transactions.
State actors paying their civil servants isn't evidence of capitalism, or wage labor.
( David Graeber does write about ancient Greek city-states and how their coinage came to be, according to the historical and archeological record, in "Debt: The First 5000 Years," by the way. )
Capitalism, is a relatively modern phenomenon, with a pretty common, well understood definition. This isn't a heretical or radical idea. You may find some societies prior to the 16th/17th century that fulfills some characteristics of capitalism, but they don't make the cut.
People naturally want to trade. Markets existed before capitalism and they will exist after capitalism.
This smells like "socialism works fine it just that all the failed attempts were doing it wrong".