Primary exports are not owned by the government, that is mostly private. Primary imports in natural resources domestic oriented businesses might be state owned, as are companies that produce primarily for the domestic market (like SOE JV car manufacturers). All those little factories that produce for export are very private.

The communist party doesn't really follow any tenants of Marxism at all. Most are only concerned with propping up their families and embezzling enough money to send their kids to a nice school abroad that doesn't suck.