All Mine.

She would have preferred to join in the fight and kill Aeternus. She would have done just that instead of sending the snake demon king off if there was a definite chance of victory. But there isn't a definite chance of victory. She doesn't think the two of them can win against Aeternus. That means that the snake demon king is going to his death, alone. She will join in in case she is wrong and the snake demon king actually threatens Aeternus. Then the two of them can kill him together. 

She muttered in anticipation of the upcoming fight, "It is so good to manipulate others. It is almost as good as sex."

Succubi are not particularly strong demons. They have a lot of abilities related to charm, seduction, and illusion but they lack outright firepower either in terms of physical or magical output. They have to be manipulative with what they have since it is foolish to use brute strength.