Is artificial intelligence, rightly considered, an empirical science? If not, what is it?

Most of the empirical sciences you mentioned involve understanding things that already exist, rather than bringing new things into existence.

This sounds like a disguised query. What are you really asking about AI? Separate the definition from the implications; what's an "empirical science", what further properties does the definition imply about entities it describes, and does AI need those properties to accomplish its goal?

(I'd describe it more as a research program that draws from several empirical sciences (cognitive science, etc.) and sometimes motivates advances in those fields, in the same way that nuclear physics is an empirical science, while the projects to create nuclear weaponry were not empirical sciences in themselves but were research goals drawing heavily from scientific knowledge.)

Why can't AI researchers formulate and test theories the way high-energy physicists do?

Within limited domains, they do. Face recognition, for instance. You are correct that it's not a solved problem, but any new theory of face recognition, or in general any proposed computational model of the visual cortex, can be trivially tested: have it look through pictures and recognize faces, and compare it to how well untrained humans can recognize faces.

Also, reiterating a comment I made a couple days ago on a similar statement of yours:

I am not, of course, against mathematics per se. But the reason math is used in physics is because it describes reality. All too often in AI and computer vision, math seems to be used because it's impressive.

I'd find it much more impressive if you could do anything useful in AI or computer vision without math.

You seem to be jumping from "AI isn't a hard science like physics because we don't know exactly what we're trying to mathematically model" (since it studies minds-in-general rather than just the minds we can directly do experiments on) to "math isn't useful in AI or computer vision". Maybe computer vision can benefit from Riemannian manifolds, maybe it can't, maybe it's a privileged hypothesis that we shouldn't even be bothering to ask about, but do you really expect that any technical solution will be non-mathematical?