Umm, you do realize that teleport is line of sight only right (PHB 286). Your teleport is actually more powerful, since I could fey step, open a door really fast and step through. Or, fey step around corners, etc. Teleport doesn't allow you to do that.
Otherwise, cool idea.
Perhaps I should clarify - move as in only across spaces, not moving their hands and the such.
One of my players - the one playing the Eladrin that helped come up with the concept - described it when he did it in game as if time seemed to stop and, from his perspective, he seemed to float to where it was he wanted to go. All obstacles that are there are still actually there - you can't use it to exit a walled in room, or open the door while doing so, or any of that.
Again, it's a bit roughshod, but it's the best I can do with the mechanic.