Chapter two had me worried this was going all in on a pet-play fetish that I'm not personally interested in. But this chapter has me thinking there's more to it than that. I think we're exploring the transactional and hierarchical nature of relationships, with a longer-term arc of surpassing them.
Miyu works in a hostess bar, performing an identity to get sales and clients, competing with her coworkers. It breeds resentment and dehumanizes everyone. Alienation from labor, alienation from others, alienation from the self. When she meets Shiori, Miyu doesn't have a healthy way to express her interest other than domination or extortion.
Shiori is the browbeaten office worker, with a reputation for being meek and obedient. When she meets Miyu she feels inferior. Then at their second meeting she ruins Miyu's clothes, and feels she owes her to repay them, and so offers to become her Dog (In the sense that she's a dog at work, not in a pet play sense). Their relationship starts with a heirarchy and a transaction.
It's interesting how their relationship roles are informed by their professional roles. And in chapter 3 we get a hint that being obedient isn't just about submission, but also about caring. And for Miyu being 'cared for' is about more than getting money from her clients, but getting some needed emotional care. It's a way to deepen their understanding of their roles, and invert their transaction, and humanize their relationship. Nice!