(Obviously, not referring to the 3DS' pop-up visual effects.)
Last I checked, whether a game is 2D or 3D is determined by gameplay, not graphics.
For a game to be truly considered as fully 3D, it would have the following characteristics (taken from the Wikipedia article on Super Mario 64):
As one of the earliest three-dimensional platform games, Super Mario 64 features free-roaming analog, six degrees of freedom, large open-ended areas, and true 3D polygons as opposed to 2D sprites. Hailed as "revolutionary", the game left a lasting impression on 3D game design, particularly notable for its use of a dynamic camera system and the implementation of its analog control.
On the other hand, all footage from Pokemon XY shows a fixed camera, with player movement being restricted to a standard tile grid as in the previous five iterations. Some footage from what appears to be gyms or other indoor areas even show the traditional top-down camera view.
Phantom Hourglass, Spirit Tracks, and the upcoming A Link to the Past 3D all have full polygon models, yet player movement is restricted to a single plane with a fixed, top-down camera. Some people call them "2.5D" due to their polygons, but they're not truly "3D" because they simply don't offer full 3D gameplay like Ocarina of Time.
GameFAQs.com: Where YOU make the content, but CBS makes the money. http://lueshi.info/Mario_Zelda_Tier_List.gif
Those are not the qualifications for 3D. Those are the features of Super Mario 64. 3D = polygons, plain and simple. A sprite is a two dimensional object. There is no depth. When you use polygons, it gains the third dimension(it has both x, y and z planes). That is literally what 3D is. The rest of it are just features of one video game. Take Pokemon Snap for example. Can't free roam, 0 degrees of freedom, no open ended areas. Yet it's still a 3D game. :)