Of course the actual "Word of the Year" is not emoji, but an emoji: the tears of joy one, which we don't seem to have available in our forum repertoire. Since it's not composed of letters it isn't eligible for Chi.
However, this is not to deny that the word emoji probably should be admitted. In fact there has been a daily puzzle, in 2012, which included the letters of the word, but the mandatory letter was not one of them, so nobody would have been prompted to suggest emoji. I'll leave it with you a while longer as an exercise, but to help you a little bit, it was a ten-letter puzzle.