It doesn’t matter what you call it, capital is the same thing regardless of its ownership structure. Let’s call it woogum and the woogumist system if you like, that doesn’t change anything.
Capitalism is commonly defined as a system of economics based on private ownership, and associated rights such as free exchange of labour, free markets, etc as against state ownership. Systems based on cartels, oligarchies and corporatist systems aren’t capitalist because the oligarchs, corporatist entities, etc become part of the state system. They assume powers normally the prerogative of the state. Obviously there are different degrees, no two systems are identical and all such systems have some level of private ownership and trade. It’s all a matter of degree. Even the Soviet Union had some level of markets and private exchange.
You're just restating your definition of what you define capital to be and my point is that some qualified people disagree on that definition. You can call your definition 'woogum', but the fact is that there's no book called Woogum, yet there is probably a book called 'Property' and I'm certain there's a famous one called 'Capital'.
'As against state ownership is an interesting bit to use as part of the definition, because it creates the whole rest of your argument for you (by which you must say that a term like 'state capitalism' is nonsensical, but I disagree). This is fundamentally an issue of definitions, and I'm more than happy to agree to disagree on that, or even to go with your definition, and I'll use capital-prime to denote what I'm talking about.
However, according to Wikpedia (quoting Samuelson) capital is "those durable produced goods that are in turn used as productive inputs for further production" of goods and services" - so while a subclass of property, certainly not 'just property'. This also raises an empirical question, that is, in a given society what are those 'durable produced goods...' as they exist in the macroeconomic sense? Yet others view capital as a social relation. I'm saying there are multiple perspectives on the definition, but that's the nature of multiple interested parties talking about a politically, ideologically, and socially charged subject.
I think it's an unfortunate historical accident that what we generally refer to as capitalism, the mainstream economic system in place in the western world and in fact most of the world, has that name without a distinguishing qualifier. That's why I don't object to the term state capitalism, which is a much more descriptive term.
Ideally what we call capitalism would be consistently referred to as something like free market capitalism, or private property capitalism. I know those terms exist and are used, but very often we refer to the mainstream western system as just capitalism without qualification. So people will blame 'capitalism' for things like poverty or exploitation in the west, as though such things are completely unknown in alternative economic systems.
Capitalism is commonly defined as a system of economics based on private ownership, and associated rights such as free exchange of labour, free markets, etc as against state ownership. Systems based on cartels, oligarchies and corporatist systems aren’t capitalist because the oligarchs, corporatist entities, etc become part of the state system. They assume powers normally the prerogative of the state. Obviously there are different degrees, no two systems are identical and all such systems have some level of private ownership and trade. It’s all a matter of degree. Even the Soviet Union had some level of markets and private exchange.