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.