All squares are quadrilaterals and all cubes contain squares, but a cube is not a quadrilateral, it merely looks like a quadrilateral in some projections. It may look like a hexagon in others.

Game recognize game, that was an excellent response.

I'd just point out that there has been a decades-long crusade against socialism in the west, starting during the WWII and through the cold war, and the "socialism = state run economy" shtick comes from confused westerners who've bought into the red-scare propaganda. A lot of people feel quite comfortable imagining the USSR and Moaist China as the idealistic image of what socialism is, because it's quite easy to write them off as failed "authoritarian" projects (a lot of reasons for those scare quotes, but I won't go into it). Fair enough that you don't want to be associated with that scary image, but all I'd say is that by avoiding the word with all its nuance, you loose the detailed and rich debate about it that can inform how one could approach a socialist system of organization, even the one you just described. And as long as we're stuck arguing about semantic definitions and being pitted against one another, we're not effectively unifying under our common interest, which would be the end to private ownership over the means of production.