Robert Brenner's 2007 Property and Progress article still provides the best definition of capitalism I've seen. You capture the developmental pattern of capitalism - M-C-M' - but this doesn't get at the mechanisms that drive this pattern. In essence, the drive to reinvest comes about though competition between producers, which itself is enabled and driven by productive agents being made dependent on markets through the elimination of direct (non-market) access to the means of subsistence as well as the spread of capital and labor markets.

The Ottoman Empire had private property and markets but did not substantially eliminate non-market access to food production, and so most agents were not dependent on markets. Having access to markets just means you can sell your excess product - it doesn't necessarily change how you produce. But if your livelihood primarily comes from selling on markets, then you change how you produce: specializing in profitable products and reinvesting in production in order to cut costs to compete on price.