Good point. Companies like Simon Property try to claim that their public shopping centers and malls are private property when it benefits them, but public places when that benefits them.
They have little ability to enforce their supposed rules, and they certainly have no relevance in this situation.
Did anyone at Newsweek complain about BLM protestors violating the rules posted in private businesses during the BLM protests and riots?
They DO have the ability to ask local LEO to inquire of each visitor to enforce the policy but that would be a private contract.
This would present a conflict of interest for any LEO that wants to be paid under the contract with the private entity.