Because the new DM app would integrate directly with Twitter, it could automatically display tweets from a conversation’s participants in the thread itself. This is a simple feature, but one that other messaging apps also could not offer, and it would give users additional context in a variety of conversations. For large groups that outgrew the constraints of @-replies, these embedded tweets would make it easy for users to see what had already been said. For small groups, these embedded tweets would enrich the conversation by giving a sense of what other participants were thinking about.
A stand-alone Twitter chat (DM) app by itself isn’t that interesting. But an app that allowed you to easily injected (public) tweets to chat about could be very interesting. I know I already do this in other chat apps — that is, paste in a link to a tweet and then talk about it with a smaller group of people.
Also interesting: a chat app that injected your own tweets into a conversation to kickstart dialogue with friends.