>The real goal of capitalism is to increase the amount of capital available. This fundamentally is not possible via exploitation alone.
This is a common view, however it was also a common view of the political economists before Marx published his critique of the field, Capital. It was his thesis that through the cycle of circulation, M-C-M' is observed, that is, the capitalist manages to leave with more money than what he started with at the beginning of the exchange. He turned what you have just said upon its head - one of the sources of profit is actually via exploitation alone, that is, the purchasing and usage of labour-power whose use-value takes the form of labour which is applied to the final products. It is value-adding. This is the contradiction that Marx aimed to solve, that is, if values are traded for values, how is it that the capitalist is able to make profit? Ending up with more money at the end, barring any kind of trickery or scamming, barring the fact that the economy does not solely run on collection of rent and interest, how can a profit be made?
It's probably false to describe it as a zero-sum game, but that's only because both the worker and the capitalist benefit from the trade of labour-power for wage (assuming equal values are traded for equal values, the contradiction of labour and capital in incessant dialectical movement). It is clear however that the benefit of the capitalist is indeed greater and sustained by the fact that most workers must sell their labour-power to survive.
This kind of analysis is extremely unsettling to capitalists, as value is not merely an outward appearance of a thing, but rather it is an essential quality, it is hidden away but works "behind the backs" of both the capitalist and the worker. In this sense, Marx notes that "they have acted without thinking first". One contributor to ignorance of capital and money is commodity fetishism, a term Marx borrowed from social anthropology, in which people are merely representatives of commodities rather than alienated people trying to survive on the "free market".