Cute, but sadly not real.
snopes.com: Escherian Stairwell
From the above link - In April 2013, Internet users were puzzled and amazed by a video from the Rochester Institute of Technology (RIT) purportedly documenting the existence of a so-called 'Escherian Stairwell' (named for the Dutch graphic artist M. C. Escher, famous for his "impossible reality" artworks, such as the never-ending Penrose Stairway) which "violates the laws of physics and basic logic by looping back into itself."