Being given charge of his Divine Mother’s affairs in the Temporal World,
Being Yelm’s deputy in the Mundane World, and
Being a god in his own right.
The Red Emperor is charged with provide peace and order to the whole world. Now that doesnt mean he needs to govern the world – he’s perfectly willing to acknowledge clients and allies, and let them govern themselves. But they need to acknowledge his supreme status. Independent states outside of this system are fundamentally illegitimate- they are rebels against the divine order. Sartar, the Holy Country, the Voor-ash, Praxian tribes, Loskalm, they are all the same.
One question is the status of the Elder Races. Some Lunar philosophers claim they are doomed, but the Red Emperor generally has a live and let live attitude towards the trolls of the Blue Moon Plateau (even granting them the status of Ally) and the Yolp Mountain Trolls. Same with the dwarves of Jord and the Brass Mountains. And the Red Emperor often speaks of friendship towards the elves (which is usually ignored by them);
Another question is Ralzakark, whom the Red Emperor treats as a peer. Some anti-Lunars claim that may be tie of kinship….
Importantly the Lunar Empire has no “fixed” borders or boundaries other than the Glowline itself.