QH6CH!! For me, the greatest appeal of Carlsen’s last move is the drama. When Carlsen made his move (Qh6ch), he was facing several different threats of checkmate ON THE NEXT MOVE. (Black could checkmate by moving his rook to a1; by moving his queen to e1 or f1; by moving his queen to g2.) Carlsen’s final winning move was the only move he could play to avoid an immediate loss.
The game was poised on a knife edge. Karjakin was one move from winning—when he lost.
Of course, as Gaffney points out, Carlsen had to have seen the possibility of this position arising several moves before.
Gaffney’s article has a good illustration of the final position.