It's a globe apparently according to GRR Martin. The title sequence is just to look cool. TV show also has comets.
But how would you have night time inside a hollow sphere?
In this setting people leave on planets and moons within the Dyson Sphere. It's not a Hollow Earth setting, a Dyson Sphere is the size of a solar system in this case with hundreds of inhabited planets and moons inside.
Living inside a hollow sphere isn't a new idea in fantasy. Nehwon (Fritz Leiber) is this kind of world, as is the world of Game of Thrones.
The idea is an alliance of multiverse traveling alien races, with extremely advanced technology discovers for first time that in some universes magic exists big time.
So they build a magical Dyson Sphere around a young sleeping Sun Titan to study magic isolated from the rest of the multiverse. Its basically a giant magical lab.
I think you are incorrect on both counts. Where, for example, did you find that Nehwon is such a world?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.