Spells that have no "defined shape" have the area they affect specified in the spell description. And, remember the general rule that spells do what they say they do.
Spirit Guardians has the following Range property:
Range: Self (15-foot radius)
So it explicitly has a radius and could thus be either a cylinder or a sphere. It actually probably doesn't matter which one, because of how the spell is described.
First of all, don't get too hung up on the fact that the spell "calls forth spirits"; they aren't creatures and don't have any characteristics, so worrying about whether they fly or not or how far they can reach is pointless. The spirits are a special effect of the spell; that is, a description attached to the spell that, while interesting and evocative, doesn't have a game-mechanical effect.
The spell halves the speed of creatures in the area, and causes them damage on their turns. The 'area' is the space that's within 15 feet of the caster. That's it. For making rulings about whether someone nearby is or isn't affected, you don't need to think about whether spirits fly or not; just decide if the creature in question is within 15 feet of the caster.
Most of the time, the "sphere or cylinder" distinction won't make a difference here; it only matters if characters are flying and occupy a position that's close to 15' in the air and also close to 15' horizontally distant from the caster. But it doesn't break anything for the DM to just say that's close enough to be affected by the spell.