The King reincarnator isn't concerned with "winning" or "losing", especially in regards to this kingdom. In fact, he probably has zero intent of actually ruling his own kingdom/empire. His sole intent is to eliminate the threats to his people and secure food for his starving people. That was the original reason he sent his troops to invade: to hunt down the escaped nobles and secure food (via pillaging).
Here, the other king has offered him a "better" solution that doesn't involve an ugly war and loss of life. By surrendering and submitting to this king as a vassal state, the (former) Domino Empire will have access to food and aid provided by the kingdom, and the escaped nobles will be handed over. The last descendant of the imperial family will remain under the protection of Kingdom high nobles and the Babyfaced Sword Saint (and the other heroes), thus keeping her out of the hands of any other rebels. There, said descendant will be raised properly with the compassion and diligence of Kingdom nobles instead of Domino nobles.
Rain is currently NOT a threat to his people. However, she COULD be IF she falls into the wrong hands. Thankfully, she is in very good hands, and it is VERY unlikely that rebels would get their hands on her (courtesy of her peerless papa).
Thus, there is literally no reason for the King reincarnator to actually fight the other reincarnator heroes or attack Rain.