But it is not a creature and does not have a move speed at all. In terms of movement it is more similar to a Flaming Sphere or Spritual Weapon than it is to an Orc or Human.
Flaming Sphere is very specific on how it moves across surfaces (i.e doesn't fly).
Spiritual weapon uses wording almost identical to Unseen Servant and it is generally assumed the SW can can move in any direction (i.e. it can fly):
SW: As a bonus action on your turn, you can move the weapon up to 20 feet .....
US: Once on each of your turns as a bonus action, you can mentally command the servant to move up to 15 feet ....
This is almost identical wording.
The main argument that it can't fly comes from the fact it "springs into place on the ground" which implies it has to rest on the ground, but then it has no discussion on how it moves over barriers or across surfaces like Flaming Sphere does. If this is the intent it is poorly worded IMO and leaves a lot to interpretation.
Spiritual weapon: "You create a floating ..." is not the same at all as something that shows up on the ground and otherwise has the same capabilities as a human servant.