That really doesn't change anything significantly. Consider the kind of game this is. You are meant to play the game over and over again. It might not be a rogue-like, but it has a similar expectation that you'll play many games of it instead of only once or twice before setting it aside for years. In a typical game (we'll say RPG since stories are very common in them, including branching stories), having multiple endings or branching stories provides replayability because it gives you something to work towards, even if 95% of the game is the same. The expectation is most would probably play 2 or 3 different ways to see different endings and then set it aside for awhile before possibly trying other endings/branches. Because of that, it adds those extra couple games worth of replayability and works well.
Now, look at this game. Most players, if they like the game, will play dozens of games already, without any story. Add a story and what do you get? Something you are interested in the first time you play, but then don't care about. That doesn't improve replayability unless it draws someone back for a game when they had no intention of playing the game anymore, which would be a pretty low percentage of players, and not those who are regularly playing the game. Add a story with multiple endings and what do you get? If you're already playing dozens of games, you'll play the different endings and then there's no reason to care about them again because you already know the stories. That doesn't increase replayability because you would have been playing those games even without the stories. Again, only those who are no longer playing the game but are interested in the stories might come back because of the stories for a number of games up to the number of story endings or branches before setting it aside again. And again, that's a small percentage of players, and doesn't include those actively playing the game. For this game, a story of any kind, regardless of branching or multiple endings, won't have any real impact on replayability. The game is already very replayable and a story doesn't really change that.
I'm not saying they shouldn't include a story, but don't expect it to have any real impact on the game beyond just answering some questions we might have. There is also a good indication that the story may be limited to Navesgane and not RWG or custom maps, though that hasn't been confirmed.