Thanks. I'm aware of all those uses. But that strongly suggests that he's constructed a simulation of projective / elliptic 3-space, not spherical 3-space. The image on the screen is a perspective projection thereof.

Additionally:

To clarify my understanding of projective vs elliptic geometry, because I keep conflating them: Projective space is a topological space, while elliptic space is projective space endowed with a certain metric, turning it into a metric space. Additionally, every elliptic isometry is a projective symmetry, while the other way round isn't true. On a purely topological level, there's no difference between elliptic geometry and projective geometry.