It's very unlikely that a game would take its final shape by linearly expanding from its narrative beginning to its ultimate ending. During the development, some pieces of the game are developed as modules and all these modules are put together when a playable of some sort is required. But maybe after the Alpha is out, some extra iteration is required to sort out problems and those pieces need to be re-shuffled for the Beta or the next version. Again, it is possible that this task would come at the last moment.
Depending on the size of the project, the designer might have a big responsibility in putting everything together. Usually, the designers are in charge of setting up the whole game content. Maybe the beta version included only a single level or mission, and that one was put together as best as possible for the Beta phase. Now it is time to create and introduce the rest of those missions, quest, dialogs, characters, and levels.