Why would they need to write an app just to let you stream stuff from the iOS app? That's just "AirPlay".
That's not what this would do. I think there's a weird game of telephone happening here. TechCrunch said, "broadcasted from Twitter’s Periscope app." Which Macrumors translated to "watch content streamed from the Periscope iOS app."
This will all be done natively with no connection to a phone, because obviously. I think MR added a word that made TC's slightly confusing statement even more confusing, to the point of your question.