You're comparing the "right to private property" thing to capitalism and communism, and considering it from the economic vantage, which is precisely what the OP was saying isn't what the term was for.
Compare it to feudalism. "You're allowed to have things that are yours, and the king can't just take your farm".
There are certainly systems that can be described as free that don't acknowledge the concept of exclusive ownership, but they usually have to carefully define terms to handle why you can't take your neighbors wedding ring while they're showering.
The term is not without economic connotations, of course, but that part was not meant to imply a specific unlimited right. You could address everything on your list and be well within the definition because "you can have possessions" isn't contradictory with public ownership of scarce or critical resources.