Conservative Man - Though I did not read the entire article, I did read enough of it to see where they were going. Essentially, there are a bunch of communes on which everyone lives (or if not, is forced to work as a farmer for all practical purposes since without money, there is no useful medium of exchange) and somehow contributes. There is therefore already a "government" as the commune seems to have the ability to accept people and boot people out (thus it is a pure democracy mabye?). I was not really sure how relations among communes were managed (so could I take over another commune by force, or is there another government layer that stops me?), but it appears to me that without a real government you would more or less get mafia style government eventually (since you can't eliminate those sorts of people and with no opposition, they will rise to power eventually).
Also, your specific statement woud directly violate the Nash Equlibrium of the state in which nobody works. In a state in which everybody does nothing, if I do work while the other person does not (but that person is still able to enjoy the fruits of my labor), then I have little incentive to work because I can just assume that the other person will do something (while I will not). Also, if I work and the other person does not, then he/she gets the fruit of my labor, but conbributes nothing (which I will not be happy with).
In addition, the "productive" state is not a Nash Equilibrium (thus not stable) because if just one person stops working, then nothing bad really happens, so the incentive for every individual person is to stop working because everyone else can just pick up the slack.