They're not actually engaged, they're just living together. But if they weren't in a relationship, then the cheating path wouldn't make any sense. The game is about Ria's desire to become a professional singer, and the compromises she has to make, to become a star. Plus, she's being deviously manipulated by Carl to become sluttier, so she can convince Promoters like Thomas to help her get to the top. And all of this has consequences for her relationship with Ted. That's what the games about, and if they're not together, it would just be meaningless.
I guess you don't like games with cheating content. Unfortunately, that's an essential part of this one. Because you can't have a cheating path, without cheating. Despite cheating on each other, both characters still love each other, and I'd like to think there'll still be a way for them to stay together ( via an open relationship)? But I imagine it will be a rocky road to get there.
I suppose also them splitting up might become an option as well, or if you have them remain mostly loyal on the Love Path, they could still end up having a conventional relationship?