Eh, I'd have to say it's a bit more than just a story once you look at how it influenced how many people view life, and act in it. Many stories do this however, so ST doesn't deserve some shining holier than thou medal or some shit.
You guys don't get it, don't see to the level you should see. It's certainly unique, and it has a unique message that I've never seen before, in any medium (at least when it was released). You can argue about what construes as scifi, but that's not really the point. Up until ST, I've never seen a piece of fiction that had such a glimmering aspiration, raw hope, and positive message about the future of humanity, of all of us. Tell me of another one, in books, movies, or otherwise.
Every piece of space science fiction is almost always wholly the same. It's some ultra fascist, para-militaristic bleak future where the only hope for humanity is xyz, or some type of cowboy-ish western type with ships and mercenaries. ST has always painted a world with a very unique brush, and this brush paints humans that are essentially almost perfect. They've overcome the common vices that we struggle with everyday, from personal vices to societal ones.
All of our issues have been mostly solved in that universe, but the best stories in the ST universe are about how those problems, no matter how close to perfect we get, still try to come to the surface, like that Lessons in Humanity: Habeas Corpus clip I posted. ST was powerful in that it wasn't just social commentary on our society (which the new ST and most new fiction isn't even this) but it says
how we should aspire to be: what type of person, society, should we aspire to become. To me, that was always the core of Roddenberry's vision. It was never about a scifi story, but an aspiration told through one.
The new ST isn't garbage when you compare it to other garbage released today. It's garbage when you compare to what it should be.