Just move your section C in front of sections A and B below the wainscoting (chair rail) and you've got it! Section C would be an odd shaped wall...not rectangular but more "square U" shaped.
C can't be U shape because you'd see it as the mirror moves both wide and down at the same time. Again, the only way that would work is if there is nothing behind the mirror where it grows horizontally. For that to work, the mirror can only grow the width of the mirror's frame sides. Else, you'd see the gap when the mirror is in the start position or you'd see the U shape when it was opening.
Trust me, I worked through this as well and was my first thought because of the chair rail piece made it seem obvious as a place to hide a seam. I was also thrown when the chair rail wasn't atthe bottom of the mirror.. but like Rob posted, it's actually aligned with the top edge of the mirror frame which is more than coincidental
Looking at the video again (now that I'm at the computer), it would appear the mirror only grows horizontally LESS than the width of the mirror frame.. which was the requirement for this to be.. So it is quite possible to only have C move, be U shape, and the U is actually the size of the final opening.. with the rest of the space simply being covered by the mirror frame iself.. and no wall at all. Nice eyes @Rob562 - the dimensions seem to work for this as I look again.
Let me do a new graphic..