Claiming that A, B & C is the same as D surely needs to imply some concern about the actual meaning of D, no?
Pretty sure what I wrote was understandable for most. You probably also understood it, but felt the need to complain about the vocabulary.
The first two may be a necessary precondition for capitalism, but they in no way describe it - they are common elements in human communities that predate capitalism by millenia.
(1) says rewards are assigned based on supply and demand. If labor is scarce and investment is plentiful, rewards will go to labor. If investment is scarce, and labor is plentiful, rewards will go to capital (with the obvious caveat that there are many other factors that affect returns, and their distribution within the pools of labor and capital).
Unfortunately for western labor, there has been an exploding world population and lower barriers to trade & investment flows (globalization) for the last 40 years - hence a huge glut in labor. Rewards have gone to mobile capital, tech businesses and workers in the developing-world, not so much to blue-collar work in the west. But that is mostly supply & demand, not a built-in rule of capitalism.
There are certainly other ways of distributing the rewards, no question about that.
So the question arises: why do the rewards go preferentially to capital in so many of the ventures that exist in our system? Your argument claims that it reflects the (relatively) low supply of capital (compared to the (relatively) plentiful supply of labor; we'll ignore IP for now).
By contrast, I claim that it doesn't reflect that primarily, but is instead deliberate economic/political/legal choice made under significant influence by capital, and that's why we call it "capitalism".
If we lived in a world, for whatever reason, the rewards of a human venture went primarily to labor, we can still recognize that there's a "system" distributing the rewards, but we would not call that "capitalism".
So I'd partially agree with your argument but then invert it: an important reason why the rewards go to capital - i.e. we live in a capitalist society - is that there's sufficiently little countervailing pressure on this arrangement. How much this comes from population numbers, lack of political will, schemeing by the rich etc. is always going to be hard to say. However, a system that didn't work the way ours does would not be capitalism.
Wage-based employment is certainly an economy. It is affected by laws, taxes, regulations, wage transparency, negotiating power, unionization, social welfare benefits, etc. But in the western world, it is approximately a market, and wages are affected by the supply of labor (with skills/without; with education/without; with an artisan skill/or not; prepared to do dull, repetitive, smelly, disgusting job/or not).
How is labor not a market?
And do you know workers with profit sharing, or performance-related bonuses, or share options? Well they are essentially capitalists in their own employer, with some (small, perhaps insignificant) share of the returns to the business.
Do you know anyone who is self-employed? They are solo capitalists, self-started, owners of their shop or tools, and a capitalist of one.
Do you have a pension that owns equities? You are also a capitalist.
You may hate your manager, or envy them, because they earn more than you, and get to boss people around. They are not capitalists. Managers are not capitalists, don't confuse your hatreds. They are only capitalists to the extent that they also get share ownerships and options. Choose your targets carefully, and be explicit in your class-warfare hatreds.
For a system to be capitalist, it requires additional features, and the most significant of these is the way the rewards of human ventures are distributed (i.e. primarily towards those who invest capital rather than labor or IP in the venture).
Nope.
Capitalism, at least 21st century western capitalism, consists of 3 things:
1. relatively free markets, in the sense that what can be bought/sold and for how much is only loosely regulated
2. an entrepeneurial culture that supports the idea of "starting a business"
3. the idea that the rewards of any given human venture should go primarily to those who invest capital (rather than, say, labor or IP) in the venture
What you've just described doesn't specifically cover any of these three, and it particularly doesn't cover #3 which is the most pernicious aspect of capitalism (the other two could exist in a system that did not incorporate #3).