You cannot engage in trade, negotiate prices, hold an auction, and make meaningful choices with money without a property right mechanic. A property right is the right to do or to not do something; to posses a privilege you can elect to use or not to use. To clarify what this means I will pull some examples of the use of property rights from the real world
Property Rights in the Real World
From your own personal intuition, if I said you owned a car that means something to you. That means you have the privilege to drive your car to Kalamazoo (granted you also have the privilege to put gas in your gas tank to run your car). You also have the privilege of choosing to put it on cinder blocks in your front yard and use it as a lawn ornament. Owning the car means you have the privilege to elect different ways to use it.
Ownership means you also have the power to exclude someone from using the car. If I want to drive your car, I need your permission first. You can exclude people from repairing the car. A mechanic cannot repair your car unless you give them permission to repair your car.
Not all property rights come from straight up ownership of a good. Sometimes, you can have property rights over an object you do not directly own. When you rent a car you do not own the car. However, you still hold property rights over it. You were granted a lease that instill upon you privileges you can execute. These privileges, such as the ability to drive the rental car, are your property, even though it may only provide you with a set of limited temporary actions.
Why Are Property Rights Important
Property rights enable people to voluntarily interact with each other. All interaction is a form of trade, even a conversation. If I start talking to you, you have the privilege to select what you can do, you can elect to listen and engage me in conversation or you can elect to walk away from me. To have a conversation, my talking has to be valuable enough to entice you to trade to me some of your time instead of you using it to pursue a different activity.
Without trade, there is no need for money, there is no need for auctions, there is no need for prices, there is no need for interaction. To trade, you must be able to confer to a person a privilege, a property right, be it a good or a service. For example, to acquire the privilege of me rubbing your back, you must exchange with me a privilege I desire, say the privilege of driving your car for a day.
Imagine a world without property, a world where you no longer have the ability to grant or not grant someone the privilege to undertake an action. In this world, you do not have the property right to choose where to drive your car, you do what you are told. You do not have the ability to choose whether or not you give someone a back massage, you are told to and you do it.
Some people will call this world an extreme version of communism. I personally call this the game of Candy Land. You do not decide where you move your gingerbread man, the gingerbread men overlords have instructed you where you will be. The gingerbread men overlords dictate who will be granted permission to stop walking around in endless circles and finish their trot to Candy Castle. In Candy Land there is no property, there is nothing to trade, there is no need to hold an auction because players do not own any privileges they can exchange with other players. Without property rights the only privilege that exist is the privilege to exist, the privilege to play the game.
To be honest, I want more in my gaming experience than just the privilege to play. I want the privilege to make meaningful decisions, preferably with some sort of trade and price mechanism involved. I can only have this experience if the board game, if my life, includes property rights.