[zenorogue]

Unfortunately spherical geometry is often done incorrectly (in Civilization the Earth was a cylinder, in other games planets are tori).

What kind of shooter? An Asteroids-like game on hyperbolic manifolds (both 2D and 3D) can be found in HyperRogue, although there is no gravity. Gravity in hyperbolic space is a rather problematic thing, you always get some extremely weird effects, also I believe there are no stable orbits in hyperbolic spaces.