I star trek into darkness.
He/she/it star treks into darkness.
We star trek into darkness.
They star trek into darkness.
Now it's a verb.
In those sentences, yes. But "Star trek into darkness" has no subject, so it's not a sentence with a verb -- again, unless it's an imperative and the implied subject is the listener. And "Star" could not be the subject with that form of the word "trek" and with no comma. If it were "Star treks into darkness" or "Star trekking into darkness" or "Star trekked into darkness," then it would be a verb with "Star" as the subject, but not in the form "Star trek into darkness."
By analogy, think of Voyage to the Bottom of the Sea
or Journey to the Center of the Earth
. "Voyage" and "Journey" aren't verbs in those titles, but nouns. They aren't imperatives telling the audience to voyage or journey to those places; they're simply a description of the events being depicted in the stories. This is a movie about a voyage to the bottom of the sea, this is a book about a journey to the center of the earth. And equivalently, the show Gene Roddenberry created is a television series about a star trek -- i.e. a long, arduous journey in space -- while this movie is depicting a star trek into darkness -- i.e. a long, arduous space journey that goes somewhere dark. (Like, maybe, space?)