Capitalism is simply where private individuals own the "means of production" (factories, tools, land) and operate them to accumulate profit.
That is private as in not lords, guilds, cartels, governmental authorities, tribal leaderships, etc.
There's a lot of stuff people conflate with capitalism like free market economics, currency, share based companies, free mobility of labor, or debt instruments of any kind.
Capitalism does require a market so goods can be exchanged, that's all it requires, and there's enough flavors of capitalism thanks to the different countries in the world that this distinction isn't superfluous.
This is capitalism, as demand increases, so does price, regardless of the cogs.