The problem of the Nephite teaching of a future atonement is that it would seem to require that humankind had to wait upon the ability to repent. If the Messiah was so far in the future, it did no good for those living in that present time. Therefore, humankind lived according to the laws that they knew.
One place where Korihor appears to differ in his preaching is that he was not only anti-Christ, but also anti-Law of Moses. Korihor does not preach a return to what others had taught, which was that the Law of Moses was sufficient, but rather that “whatsoever a man did was no crime.” This took the concept of the lack of a current atonement (and only one that was expected in the future) to a rather extreme end. If atonement only happened in the future, then it really was not needed, and it was not needed because, without an atonement, it didn’t matter what one did.
Where the typical anti-Christ at least taught that an understanding of Jehovah’s laws was important, Korihor appears to preach that religion itself was not required. He taught that there was no future atonement, and no existence after death that one had to take into account in guiding one’s mortal life.