Alexander believes that he will succeed in influencing Airin and making her feel guilty. At first, he thought he would give anything as long as he got his crown again but now it's different because he doesn't want Anthony to get everything including Airin.
Airin only needs to kill Anthony, she doesn't need to marry him. Even though he doesn't have any feelings for Airin other than ambition, there will be no one more worthy of accompanying him on the throne if it's not Airin. He needs a beautiful and tough woman, Airin has everything he is looking for as a companion and makes him invincible especially now that he also feels threatened by Widuna.