If I could summarize your argument, it's that because workers owning their company in a capitalist society does not disqualify that society from being capitalist, there must be something more to the matter than workers owning their company. This is correct: worker ownership of the means of production isn't a comprehensive definition of anything, but rather a specific demand socialists have made. I'm of the opinion that the core of socialism is a critical view of the wage labor relation, being that this is the only thing all socialist groups seem to share. That is, it's a dislike of the dependence that is developed by those with nothing to sell but their labor on those who own the means of production, arising from a property regime in which labor is kept divorced from investment. This is why Benjamin Tucker describes socialism as the view "that labor should be put in possession of its own." If every business in the marketplace were owned by their employees, and thus there was no operational distinction between "they who labor" and "they who own capital," would this market be a socialist one? I imagine many would say so.

The description of socialism you offer is "[the proletariat's] complete dominance in society." I'm confused at why you don't mention a term so often used for exactly this: dictatorship of the proletariat. This describes a period during which the lower classes have somehow become the ruling class and are distributing ownership of what was controlled by the previous ruling class among themselves. But this process would be only a means to an end, not socialism itself.

I should also mention that your characterization of capitalism, with the bourgeoisie simply as "entrepreneurs," is so laughably wrong that I don't even feel the need to address it any further than by calling it so in this very sentence.