So here's my interpertation: the leash and the rope are both red strings symbolizing the characters need for connection. They both have trouble emotionally connecting with others and use the play to bound others because they're afraid of being left alone. For them it's not about sex, it's about emotional fulfillment. .
Most people associate bondage and pet play with sex, so they can't find a suitable partner because other people don't "get it", thinking it's just kinky sex and so don't give what they really need, which is emotional connection.
Only together they can truly get the catharsis they need, because their play is not sexual, but a way for them to emotionally bond. It doesn't mean their relationship can't be romantic or sexual, but the play itself must be divorced from these kind of things.