* wage labour being the dominant mode of sustenance
* a class structure still visible (in fact, is seems as though such a "Socialist" mode of production would have even more well defined classes than our current mode)
* private property, but rather than being owned by capitalists it is owned by the state
So "workers owning" means of production is not adequate for Socialism. Rather, there must be some kind of shift in terms of how society functions in general. There should be no trade, as trade is a side-effect of the operation of the law of value and exchange value, a dialectical contradiction only found in capitalism. There should be no state, as the state is what exists to defend private property and prop up class interests. Production should be entirely for useful qualities. All productive power of society should be owned by workers (this is your "owning the means of production") either by representation of a government (which is not a state, the distinction is important) or via some other apparatus.
For these reasons I am extremely skeptical when people describe countries such as Venezuela, which operate as capitalists, owners of property, on a global scale as "Socialist". If it is Socialism then it is certainly no Marxian Socialism.