I'm a strong proponent of thinking about interesting geometries and physicses like this in games, but I'm reluctant to describe this physics as more correct than the original.

The original had correct physics for the simplest possible torus, the mathematically abstract flat one. You've replaced it with correct physics for some arbitrary irregular torus that happens to embed into 3-space :)

(In fact, you can embed the original, flat torus in 4-space, as x² + y² = z² + w² = 1. If you put that into your geodesic solver, all the weird cross terms will go away and you'll get normal Asteroids physics.)

(And now with santaclaus' comment, I'm wondering what geometry I would advocate for a double torus. It can't be flat because of the Euler characteristic or something, but can it at least have constant curvature everywhere?)

This reminds me of a game I wrote for Ludum Dare a while back:

http://0fps.net/2011/09/13/ludum-dare-21-results/

The title of the game was "Help! I'm trapped in a compact riemannian manifold"

You can grab the source for it on GitHub, though the build process is pretty janky as I wrote it in 48 hours and wasn't very careful with the distribution:

https://github.com/mikolalysenko/ludum-dare-21

This is really cool! I could really use a longer gameplay video though to get a hang of how the screen mapping works.

Why stop at a torus? Go Genus-2!

wait im confused, why a torus and not a sphere?