It's not an either or proposition. Trek has ALWAYS been inconsistent in its application of time travel--the needs of the story outweigh the needs of consistency (to coin a phrasePlease see my post above. Yes, there are other realities in the Trek story, but they co-exist. New ones don't pop up alongside the original when a timeline gets changed. This means the movie is either an alternate reality and was from the start, or the original timeline is now being overwritten.

Even if we do not adopt that extreme position, the fact remains that time travel has been treated inconsistently throughout Trek.
The fact that Spock Prime (weird to write that, but that's his character's name in the credits) affirms it's an alternate timeline is sufficient for the purposes of the film (and the franchise).
I'll go even further than that. IF it is, indeed, "overwriting the original"--it still doesn't matter. The original had to have played out as it did in order for Nero and Spock to have been thrown back and it therefore loses none of its "meaningfulness" in the process.
In the end, time travel should just be enjoyed as it is happening in the story. No matter what form or set of consequences one tries to place upon it, it will ALWAYS fall apart under scrutiny. Best not to over-think it and certainly not worth crying or mourning over "the lost original". It's all fiction and it's all available at your local or internet media store.