Some ancaps prefer the term 'voluntaryist' to describe their position. Though I think it is fair to call Anarcho-capitalism a form of anarchism because it posits no state and no rulers, though laws would still exist.
Semantically an - arkhos just means "without rulers"
It's just not. There's no way using the historical understanding of Anarchism where the following scenario wouldn't be seen as completely absurd:
"Hi HeckFeck! Yeah, this is an anarchist society, we have no state and no rulers, well, except for Fred. He owns all the Water. He inherited the rights from his great grand father that bought it for grains from the starving citizens, yeah, he owns all the land too. Anyway, welcome to Fred's coal mine, grab your hat."
However, if we limit anarchism to its more historic meaning, which is anarcho-communism and related ideologies, then you'd be correct. To avoid confusion this is why ancaps are using the term 'voluntaryism' to better describe their position.
Corporations wouldn't exist in an ancap society, as they rely on limited liability, meaning their executives are not legally responsible for their decisions. Such an arrangement can only exist under a state. (cf. https://www.opendemocracy.net/en/corporate_responsibilities_...) Holding directors accountable to their lenders, customers, investors, etc will strongly disincentivise the short-term mindset we see in corporations today.
Well, we'll agree not to coerce anyone to adopt a particular definition. ;)