What is the difference between this, and a zero sum game?
The zero sum assumption is based on "work" (as in human effort and human ingenuity) or "goods" being a fixed or certain amount. There is a certain amount of goods to go around, and everybody is entitled to some.
The point of "What one person receives without working for, another person must work for without receiving." is to criticize deliberate deficit in human effort. The grasshopper and the ant, if you will.