Ambition
Prince Raijun had made some considerable concessions, even at his own expense, that gave Rui a lot of leverage.
Of course, Rui was not fooled that he had suddenly come to have the prince by the balls if he signed this. The power disparity between them was too large. But it was a token of his good faith.
He was afraid that Rui would not give the training his very best if he felt like he was being unfairly disenfranchised in their agreement. Thus, these terms were quite beneficial to Rui.
While other prominent and powerful Martial Artists had personal staff that took care of making sure such contracts were clean of any traps, Rui didn't have such people.
He didn't need them either, having gone through and memorized Kandrian contract law thoroughly after he made the offer to Prince Raijun.