"Who runs the Planetary Protectorate?"
The Planetary Council, as the ultimate human governing body on the planet, has the authority to oversee and manage the Protectorate. To learn about the Council (and how it's elected), see the explanation of The Council Branch.
As the Protectorate is not yet fully formed, and the first Planetary Council has yet to be elected, stewardship of its duties is held by the Reminder-in-Chief.
Once the Protectorate has formed to such a degree that Land-Based Sequential Delegation (see link above) is able to produce the first Planetary Council, then the duties of managing the Protectorate shall transfer to the newly elected Council.
The Reminder-in-Chief is the one who has revived the Protectorate and built this website. He acquired the rightful authority to do so when he recognized the validity of natural law and channeled, arranged, and published its first-ever usable version: The Law of the Earth.
As the first (and thus far, only) person to publish a fully functional reference of natural law, and the first (and thus far, only) person to claim the authority to govern the planet based on the recognition of this law, his claim of being the true and rightful Reminder-in-Chief is, thus far, unchallenged.
If you have channeled and published your own reference of natural law, and it's more accurate than his, and you wish to challenge the current Reminder-in-Chief for his title, you have the right to do so. Email email@example.com, and we will have a rational debate about which one of us is more worthy of the office.
Daniel Ryan Pugatsky, the Reminder-in-Chief of the Planetary Protectorate