No, it wouldn't, because it is marketable ownership of the means of production that defines capitalism; that is, it is the buying and selling, not the ownership alone, that is key (particularly, historically, the marketability of the means of production is a key factor distinguishing capitalism from feudalism, in which much of the means of production was owned but attached to entailments which the current owners were not free to alienate.)
For a version of your example, if everyone owned a fixed, equal share of the means of production which was not marketable, that would be an implementation of socialism.