This specific app looks like it's equivalent to the 3D on a 3DS, but that's not true for 3D in VR in general.
3D from a fixed perspective (unrelated to your physical head position) on a display that is (usually) in a fixed position isn't really comparable to 3D in VR, where you have a free perspective that follows your head movement.
Think about playing a 3d-rendered mini golf game in a traditional 2D display. You indirectly control a character you see on the screen. Adding stereoscopy may make the character appear slightly in front of or behind the screen, but you are still controlling it indirectly. With VR, you are holding the club and standing on the putting green.
You say that no 3DS game depended on the 3D, and that may be true, but stereoscopy doesn't really open up many possibilities unless you intentionally remove other depth queues. There were a few bonus areas in Mario 3D Land that did that, but yeah, it that was mostly a gimmick. Virtual Boy had a fixed position as well... it wasn't strapped to the user's face.
I'd say that the stereoscopy aspect of VR gaming is less important than how it shows you a realistic position based on your head position.