Yes it is. Capitalism doesn't mean an absence of government or make any distinction between private or public ownership, it simply means that the way resources are distributed is through a market system. In order for the market to operate a means of exchange that we all agree upon and trust is required. This is money. Banks manage the market system's means of exchange. If something happens that impedes the exchange, the system is compromised.
capitalism: an economic and political system in which a country's trade and industry are controlled by private owners for profit, rather than by the state.
That's the dictionary definition. What you're talking about is "the free market" - which is not the same thing as capitalism.
If we are nit picking...
What I am talking about is free market capitalism. The definition you quote talks about trade and industry - which we can reduce down to calling the means of production. Capitalism is about ownership of the means of production for private gain. It doesn't exclude government ownership of resources / means of production or indeed and perhaps most importantly the money system. I think you could even argue that public ownership of the money system facilitates the capitalist economy. What does the central bank / federal reserve do?
