We're discussing canon so when a book is set has no bearing on it. There's no mention in the movie of a timeline splitting or of Spock & Nero hopping dimentions or of the prime universe being overwritten. Uhura calls it al "alternate reality". If I take my pants to the tailor to have them altered, I don't get two pais back, the original and one that's was altered to what I wanted, I get one pair that has changed to something it wasn't previously. Hence altered.
You're defining your terms incorrectly. "Alternate" does not mean "altered." They're related words, but not synonymous. In this context, "alternate" simply means "constituting an alternative." For instance, if your GPS tells you that there's a traffic jam on the interstate and offers you an alternate route. Or when they empanel a jury, they pick twelve jurors and several alternate jurors in case one of the originals has to drop out. An alternate X isn't an altered (changed) form of the original X, it's simply a different X that coexists with the original and provides you with an alternative (different) choice. If you choose the alternate, the original is still there; you're just not using it.
Besides, you're taking this whole thing too literally. Star Trek is a work of fiction. It's something that people make up for entertainment purposes. And that means it follows whatever rules its creators want it to follow. Nobody -- not the creators, not the fans -- has any desire to "erase" the original Trek continuity from existence in-universe. And no matter what might happen in a new story, the original TV episodes and movies and books and comics will still be available in the real world for people to watch or read. Nothing's going to be "erased," so there's no sense in worrying about it.