How can they do this? Does the U.S. rule space? Is the FAA the only authority on space travel on earth?
No, foreign companies launching on foreign soil aren't subject to these regulations.
The rules apply to American companies launching from anywhere in the world, and to foreign companies launching from U.S. soil.
They are The Government; they can do what they please :-)
Does the U.S. rule space?
Not yet, unfortunately, but the FAA does 'rule' (oversee) public and private air travel engaged in by U.S. companies and launching from US soil.
Is the FAA the only authority on space travel on earth?
No, but if you'll read the article, you'll notice that these rules apply to U.S. -based corporations and flights from US soil.
Other international agencies will likely issue rules for other corporations and for flights from other nations.
1. How can they do this?
Corporations are Constitutional legal persons created under the USA. FedGov makes the rules for all persons under its jurisdiction, especially legal persons.
2. Does the U.S. rule space?
By Treaty, the USA has asserted ownership of the entire universe, seen and unseen.
I agree, Hell they cant even look after what is going on here on earth.