Only if you've redefined "capitalism" to mean "any economic system including individual/institutional holdings and trade", in which case you've successfully and retroactively redefined all economies ever as having been capitalistic. A net that catches every fish names none.
"A net that catches every fish names none" is an interesting turn of phrase. Does it come from somewhere? Nets don't usually name things; the net that catches only 2 fishes also doesn't name them.
No, my brain just mixed metaphors stupidly. It just sounds interesting because it alliterates, which is also by accident.
I was thinking about how tuna fishermen cast dragnets that often catch many other things, up to and including sharks and dolphins. Hence, you couldn't really call such a net a "tuna net", since it more just catches tuna by coincidence of catching everything even remotely fish-shaped.
I think you missed the "free" part of the definition. The trade between the North Korean death camp guard and a prisoner is between individuals but that doesn't make it capitalistic (because of that "free" part being absent).
No Lord God Mises necessary. The rules for "pure" capitalism are the minimum set needed to allow free exchange between individuals.