We could discuss it further I suppose, but it's somewhat dull well-treaded material IMO. Anything about the definition of anarchism is up for debate of course, but completely un-checked capitalism certainly does not inherently result in a society that fits the criteria. What could possibly be anarchistic about a society full of wage slaves? That's certainly one likely outcome of such a society (note I'm not saying it /would be/ the outcome). Corporations can - and do - coerce every bit as much as the state does, if not more.
If you're an anarchist and not a socialist, fine. The term "individualist" works well. It's not the ideas of free markets and commerce, it's the /term/ capitalist. The word itself is pejorative. Anarchism is traditionally a leftist movement that came from the same kind of time and place as communism - "capitalists", the class, are the enemy, and exploit by definition. In the world of political discourse in which anarchism lives, If you call yourself a capitalist, you are essentially saying "I exploit others who actually do work as my source of income". You are NOT saying "I think free economic exchange is a good idea", which is probably what you actually mean to say. If you want to have serious discussion with anarchists, you can't call yourself a capitalist. All you will get is endless tirades about why you are not an anarchist, like this one. You might as well show up at a hard right think tank and call yourself a libertarian-stalinist.