I'm not a native English speaker but every tagline for this movie has been slightly off.
?? the taglines have made perfect grammatical sense so far, "time runs out" is a fairly common phrase to use, dont see anything weird about it or them.
It's not common to phrase it like that. "Time is Running Out" seems more sensible. Also, "Time Has Come For A New Protagonist", as an isolated phrase makes no sense unless it's linked to Inception.
Sure, perhaps the word "the" would be expected but its really not a big deal. Let's not forget that in narrative writing you normally stay in the immediate past tense ("time ran out") and "time runs out" keeps it very present tense, which could be significant.
It could also be that time is used as more of a proper noun... "Time has come for a new protagonist" makes the most sense without 'the' if we assume Time is a character (not a human obviously)