It's also sort of wrong to talk about private property in Marx's end game. It simply doesn't exist. There's personal property (your residence, clothing, non-scarce items that may, coincidentally, be used in production like a laptop or hammer). And then there's the rest. The mainframe I mentioned, in a 1960s tech level communist society, would be a means of production. It's scarce, many people need access to it to enable their work, time will have to be coordinated on it. Your laptop, even if loaned to someone else, in a world with abundant laptops/computers is still your laptop.

If it helps, software in that world is not scarce either. It's freely shared because there's no copyright or license agreements. They'd be antithetical to that world's view.