You're still trying to frame his definition as subjective. It is Star Trek, in every objective sense of the word. Subjectively, your mileage may vary, but that doesn't change the fact that it is Star Trek.
When someone says, "It doesn't feel like Star Trek," what they mean is, "It doesn't feel like GOOD Star Trek," which is a perfectly valid statement.
...
Though it's still wholly subjective as a form of taste. One can say "I don't like it, it doesn't feel like good Star Trek," and that's fine, but there are people using it to say that it doesn't qualify
as Star Trek, because of some nebulous idea of what they think Star Trek is supposed to represent.
The movie answers these questions.
No it doesn't. They just thought it would be cool to have the ship fall to Earth and be saved.
Yes, it really does. I recommend a second viewing.
Well, sure, of course it's subjective, but I honestly do believe there is some level of objectivity when it comes to analyzing a work of art's level of
ambition. TOS, TNG, and DS9 all feel very different from one another, but they are all masterful shows in their own right because they all have high ambition to
mean something, to say something, to do something
new. Voyager and Enterprise were largely failures not due simply to individual tastes - there is a factual lack of originality and ambition in the storytelling of those two shows.
Likewise, Wrath of Khan, Search for Spock, Voyage Home, Undiscovered Country, and First Contact, to somewhat varying degrees, are all more or less agreed to be the best of the bunch, due to their desire to tell a new and interesting kind of story.
Now, Abrams has changed the "feel" of Star Trek once again, just as the creators did when TNG started, and DS9, and etc - but this time, much like with the creation of Voyager and Enterprise, there is not an equally high level of ambition to do something thematically interesting or risky. He's good at the entertaining, but he lacks the will to
risk. God forbid he make a movie that tries to do something we've not seen in Star Trek before on a storytelling level. It's not that he's incapable (I assume.) It's that he doesn't have the interest.