Resident Evil took the concept of Alone In The Dark, yes, but it not only it improved it greatly, but it also brought a lot of its things to the table.
AITD had a very 'nerdy' theme, it was more of a literature geeks thing.
RE used a much more popular theme.
It came up with the 'survival horror' name, which is straight to the point, easy to understand, rather than "action-adventure game with a horror theme and survival gameplay mechanics". It's a very solid term for advertising.
The whole "play a movie" feel. This was already the case with AITD but in RE they really expanded, bet, on that and it works great. With the advance of CD format, this was when games were trying to be more like movies, RE wasn't the first, but they saw the "movie potential" games were starting to have before a lot others.
Compared to AITD, it also improved the controls, and made things more action oriented, in a very tight way. Combat was clunky in AITD, they got rid of it, and concentrated on guns. A start move, because on top of being a great survival horror, it can be a fun action game as well, which is something the AITD series tried with 2 and 3 but clearly failed at (and its other clones as well).
It also added different endings, different ways the story can unfold depending on the player's actions. Again that wasn't new, but the way RE did it was very effective, and again very influencial.
It also expanded on some gameplay mechanics to enhance the survival, like the whole inventory limit/deposit boxes thing.
Then on top of this, there is an excellent art direction, an excellent atmopshere.
And I'm just scratching the surface here. RE1 is a true masterpiece, and most of its clones, and even most of its sequels, failed to comprehend and reproduce everything that made it so great. Even RE2 for instance is missing a lot of things, and fails at others, even though it clearly tries to reproduce the formula 1 to 1.