The story was Alien: isolation was very well written but it seems like there as more to it as Matt Flier, the Web developer, and modder discovered a huge amount of dialogues and audio that did not make it into the game.
The dialogue will have no impact on the game but it does give us an insight as to what the developers were planning and working on when they were developing the game. It also helped fill in some of the blanks that the game had.
Then there is also the introduction sequence which was also cut from the game. You can download the full scripts here and read about all the additional information. While it does not really change anything about the game, you should be able to learn more about Sevastopol, Ripley and a few other characters in the game.