It turns out the sacredotes are a sub-race of humans. Cave dwellers who take vows of honestly answering any question posed to them, but forbidden from otherwise interfering in the affairs of man.
Do I have this right? The dragons are the degenerate Basics, cross bred to serve the Valley People? If so, that implies that there's a genetic war going on in which the Basics and the Humans steal each other's progeny to create the weapons used to fight the next cycle of war. It's war by janissaries on both sides.
Either way, the limited geography of the story combined with the science fiction setting strongly reminds me of a Traveller post by Jeffro. In an old issue of Space Gamer one of the grognards of Traveller explained how he turned Lieber's "A Pail of Air" into a full session adventure for a randomly rolled planet. You could very easily use "Dragon Masters" in the same way. The planet's denizens are stuck at the bottom of the gravity well, but they know all about the old interstellar empire. They have their own aims and goals and squabbles, and no ability to leave their home world. Which is not to say they aren't dangerous. Which makes this the perfect sandbox for a sci-fi game.
If the players crash landed on the surface of this planet, and needed one of the sacerdotal prayer sculptures to repair a vital ship's component, a decent GM could milk that premise for weeks of playtime. Just figuring out how the place works and discovering the hidden back story could fill up several sessions of play.
This neatly resolves one of the problems that always niggled at the back of my mind when it comes to exploratory sci-fi. If interstellar travel is possible, how do ships like Enterprise constantly stumble onto planets that don't have space ships? It's clear that most planets are inhabited by near-humans - why didn't those near-humans find the Enterprise? We usually see this from the point of view of Kirk and Spock and Bones, and the rationale for why the Roddenberryverse works that way is generally glossed over. Vance's inclusion of a possible Golden Age of Man to which the people of Aerilith aspire.
Jack Vance writes this story from the point of view of the planet-bound society, and that society is one that is incapable of, and largely uninterested in, space travel. They know its up there. They know its dangerous. They know they need bolt holes, but with nothing particularly valuable for the star-farers but their own bodies, they figure they can just hide until the aliens get bored and leave.
It works. And like so much of Vances work, it's worth filing away for potential use at your game table.