There's a little bit that can be read that way — Wyoh belongs to what she calls the "Fifth International", and says that the organization includes Communists and "Societans" (which we may suppose are some sort of futuristic socialists). The organization meeting that Wyoh has her little speech in seems to have a bit of a socialist bent and consists of lots of unions and farmers. At the same time she says "I'm no Marxist; we Fifths have a practical program. Private where private belongs, public where it's needed, and an admission that circumstances alter cases". So, a fairly minor sort of socialist. Prof De La Paz is straight-up libertarian, and Mike and Mannie are apolitical to begin with, but they pretty much follow the Prof.
The loonie revolution is about freedom — freedom from Authority, freedom of immigration and emigration, and most importantly freedom from regulated commerce. The Authority controls all imports and exports — loonies can only do business with Earth through Authority — and makes immense profits on both sides of the deal, paying loonies poorly for precious goods and charging dearly for imports. The Authority sets production quotas and assigns people their jobs. The Authority suppresses political organization. What the revolution demands is simply to be recognized as a free nation, to control its own trade (there's some talk of embargoing exports due to the ecological angle, but they seem pretty certain that with Authority coercion removed, a free market can establish a fair balance of trade), to give its people freedom, and to end the fact that so many of their citizens are prisoners — they tell Earth that they're welcome to ship their unwanted up to the moon at their own expense, but once they get there, those people will be free to live where they want, do what they want, and get on a ship right back to Earth if they so choose. At the climax even a representative farmer character says "stop shipments right now! Not another tonne, not a kilo... until they come here and dicker honestly for honest price!" which seems like an endorsement of free trade. As far as I noticed, none of your criteria for socialist ends were on the formal agenda of the revolution.