As I understand it, the star altitude is measured relative to an artificial horizon.

How did it determine "down" in a moving airplane? Was it essentially doing the high-tech equivalent of dangling a rock on a string with some dampening (in a gyroscopic cage to avoid being affected by the airplane's rotation), or something smarter?

When I looked into whether astronavigation would be solvable cheaply or somehow trivially using modern hardware, I found this a surprisingly difficult problem even on a static platform - inclinometers that would get you down to 0.01° accuracy (which would still translate to a ~1 km positional error if I'm not mistaken, roughly what a skilled sailor is supposed to be able to do with a sextant) are expensive even today.

With a moving, shaking platform that's changing position (i.e. a perfect gyro will point perfectly in the wrong direction after a few minutes of flight) and might be flying turns (which makes "down" point in the wrong direction) that seems hard to solve.