It's not - the US is pursuing an international treaty called the Artemis Accords to clarify rights and obligations, which aren't laid out in detail in the Outer Space Treaty.
If the drafting is completed under the Trump Administration, I suspect it will be tilted towards a free-for-all, but it will need buy-in at least from the Europeans and Japanese (who are building and funding big chunks of the new US moon effort) who will want some form of multilateral control.
An international treaty signed by the US is worthy absolutely nothing. They are retreating from treaties signed years ago such as nuclear weapons control, OMS, ALCA, the treaty with Iran, etc, with no consequences.
If the drafting is completed under the Trump Administration, I suspect it will be tilted towards a free-for-all, but it will need buy-in at least from the Europeans and Japanese (who are building and funding big chunks of the new US moon effort) who will want some form of multilateral control.