The difference between markets and a market economy

as specified by Arnold Kling:

Now, think about ancient Egypt, the Incas, Greece, Rome, the Muslim empire, the Silk Road, the Spanish empire in the New World, the early European empires in India and the Far East, or the antebellum South in the United States. Were there markets and was there trade? Absolutely. Did they meet the strict definition of a market economy? My sense is no.

Kling's factors of determination are: production sources, transportation mandates, and labor mobility.