This chapter lays out Yuri's motivations and mentality pretty clearly without much left to explore about her. In retrospect, she hasn't really been expanded upon since this chapter, she's only become more deranged.
Page 10 is very telling. "When I think about it, I don't even remember our homeroom teacher's face." She wants someone to need her and remember her. That's why Reiji, someone who seems desperate and backed into a corner, makes her excited, ecstatic. She needs to feel needed.