You're right, that is part of how a sadist sees their partner, but You're assuming Kou is normal and not a masochist. Which he is. Being a plaything for a sadist is the same as being loved by them. You are looking at a relationship that isn't normal through the lens of "normal". Not everyone is "normal". And we don't need to be. Being different is just as okay as being normal. In real life, you might not want to judge relationships you don't understand based on your criteria of normal. I have been a masochist for over 35 years. I have a happy, healthy life, a happy, healthy marriage and three happy, healthy adult sons. Sounds pretty "normal", doesn't it?
Really, it's like Kaiya doesn't even actually like Kou, more like he sees him as an object of affection, a plaything which he controls.