: Marx's classification of people into two groups, the proletariat and the capitalist, seen in this light, is neither *wrong* nor *right* it simply is what it is. It is a classification based on the relation of people to the means of production. The capitalist owns the means of production, the proletariat does not. : There are many other ways to classify people, and none of them are existentially *wrong* or *right* - they simply are. They cannot be judged in a vaccum, one must first have a reason to seek a classification scheme, and then judge each scheme by whether or not it is suited to your purpose.
SDF: Marx did not necessarily choose his "classification scheme" all by himself -- keep in mind that CAPITAL is footnoted on most of its pages with quotations from the economists of Marx's time (whence Marx got his categories), most prominently Adam Smith, and that, in his time, it was painfully obvious, to all, who was a member of the owning class and who was a member of the working class, especially in England where Marx wrote CAPITAL. Please read E.P. Thompson's THE MAKING OF THE ENGLISH WORKING CLASS, or for that matter any of several Charles Dickens novels, most especially HARD TIMES as it is the least verbose of Dickens' works. If the difference between owners and non-owners is less obvious to you, it is because there's a significant cultural difference between where you live, now, and Marx's England.
: Second, I would not deny that Marx's classification is, in some way, "experiential." Certainly it is derived from experience. But so are many other classification schemes. For instance, classification by skin colour, eye colour, height, shape, etc. are all experiential, and indeed far more basically experiential (and less abstracted) than Marx's scheme. Which is neither here nor there, as best I can tell.
Marx's categories are not mere classifications of people, so to look at them as such is to miss the forest for one's favorite tree. Marx's categories are designed to explain the relation of individuals to the natural world, to their labor-power, to money, to exchange as the favored mechanism of distributing the fruits of nature among humanity under capitalism, and of course to the means of production as you have already noted. I hope this link explains some of your questions.
None.