As LordLucavi mentioned, Hydaelyn is a spherical planet, which is confirmed by numerous sources, starting with the very opening movie to the game (not the End of an Era trailer, the 'opening' scene after pressing start but not having yet created a character, where Hydaelyn is shown from space as a spherical world like Earth (it was also used in an ARR pre-release trailer, a still from which is shown below):

Additionally, Hydaelyn is also seen at the end of the initial Heavensward storyline, when
Elidibus is conversing with the Warrior of Darkness on the surface of Menphina (the primary moon), and it can be seen rising above the moon's surface, again as a round planet.
Finally, the Astrolabe weapon for THM/BLM features as it's 'orb' a model of Hydaelyn with tiny models of Dalamud and Menphina orbiting it. So all three of those prove beyond all doubt Hydaelyn is a spherical planet.