So, what piece do you think the characters are?
This is my opinion:
Kaname - Black King (He is the most powerful character so he is a King and I think the Black King because of the picture of him playing chess.)
Yuuki - Black Queen (She's Kaname's fiancee.)
Zero - Black Knight (He protects Yuuki.)
Aidou - Black Knight (He appeared in a pic with Zero calling them knights and he protects Yuuki.)
Kain - Black Bishop (He is close to Kaname and I chose bishop since they are the ones next to the King and Queen on the board.)
Ruka - Black Bishop (The same reason as Kain.)
Seiren - Black Rook (She is Kaname's servant and has always been with Kaname throughout the manga. So, I think she's higher than a Pawn and I think Kain and Ruka are the Bishops.)
Kaien - Black Rook (Even though he and Kaname aren't seeing eye to eye right now, he's one of the biggest on co-existence. In the past he and Kaname have worked together to create the Night Class in the academy. Also, he raised Yuuki.)
Sara - White Queen (She wants to be queen and has talked about the game.)
Takuma - White Knight (He is by Sara's side whether he wants to or not.)
Rido - White King or White Bishop (He is still hanging around, though I'm not sure in what way, and he caused a lot of the problems in VK. I put the White Bishop as a choice because there may be an unknown villain who is the White King. I am leaning towards the later, though not sure.)
Shizuka - White Bishop (Queen is already taken. She is the cause of how Zero is, and was a major villain in VK, so I gave her this.)
Ichiru - White Knight (He protected Shizuka.)
I'm, not sure about the other characters. I have some ideas about them, but I'm not really sure. Also, I'm not entirely sure about all of this. Just my guesses and what I have deduced.