Takumi's Links
While Takumi initially felt threatened by Kinuyo, overtime that fear has bled out. Nowadays, he feels content to co-exist with her, and has no problem with taking orders from her. In fact, it'd be nice if she ordered it around more - it'd welcome that with open arms.
Kinuyo generally appears neutral towards Takumi. She thought of it as a nuisance at first, an obstacle, but nowadays she regards it just as it wishes to be treated - as nothing more than a loyal dog. She doesn't show it often, but sometimes it peeks through the cracks of her emotionless exterior - those slivers of fondness, a sign that she really might care more than either of them think.
Takumi is unfalteringly loyal to Shiori and has dedicated his existence to her. To be her loyal dog means to receive her love, praise, and attention, without needing to do anything in return to earn it. He wants to please her, make her happy, anything to repay her for all she's done for him.
Takumi is Shiori's loyal dog, and she's more than happy to treat him as such - love, affection, attention, she offers all of those in exchange for unflinching loyalty. Though her behavior is far beyond how a normal friend should act, her love is genuine. After all, for someone as lonely as Shiori, maybe it wasn't just that she saved Takumi - it could be argued that Takumi saved her as well, even if just a little.