Can anyone explain to me how capitalism works with a finite amount of wealth?

No........well, maybe a fool could.

Only a fool would assume wealth to be finite.

In spite of the fabled Karl Marx argument, we are not confined to one sealed off room with a finite supply of "marbles".

More "marbles" are being created around the world everyday.

Zero sum game. Labor increases the value and therefore increases wealth. The capitalist appropriates this wealth and pays the laborer a pittance of its value.

Wealth is not static - it grows, so the answer is that with your imaginary situation, it doesn't work.

With reality, it does.