Except that the example given is of people who privately own a company making a choice to allow their employees to take time off to serve a community function (firefighting). None of the things in the definition you gave apply: "cooperatve enterprises, common ownership, autonomous public ownership or state ownership". Nope, the companies are privately owned and the owner chooses to give the volunteer firefighters time off to fight fires. "relatively equal power-relations and the reduction or elimination of hierarchy in the management of economic...affairs" Nope, the guy who owns the company is very clearly the boss and if you do not do what he says, you're fired.
Except the volunteer fire department is still a socialist enterprise, regardless whether a firm allows their employees to participate (there are indeed benefits to the employers in this arrangement) or not. Anyone (or any firm) who participates need not be coerced for it to be socialism. There is even a branch of socialism called Liberterian Socialism, which is based on free association. For purposes here a volunteer fire department and its volunteers are sufficiently socialist, even if they otherwise work for wages in a capitalist firm.