Ryuki couldn't believe that Yui really signed it, and it was honestly too shocking if he thought about it.
As for the contract is vaild?
Well, it is. Ryuki didn't know that this world had legalized slavery. When Ayumi showed the contract, he thought that it was just a prank, so he also checked with his gift and online, and it's true. The slave system was legal in this world.
Ryuki looked at Yui, and her nervous attitude, looking down and fidgeting with her hands, was cute. Now, this cute woman was his, and he could do whatever the hell he wanted. Even if he killed her, there was no one in the world who would punish him.
This world... It is a kind of fucked up world.