Colloquial American English often uses "theater" by itself to mean "Movie theater" or "Cinema" so The theater is in the city center should be accepted.
Well, as you said, it's colloquial. And we rather don't accept colloquial answers without an important reason.
I would say that the fact that is how 99% of the population actually speaks would make it important. You almost never specify "movie theater" in US English (it's just theater or just "the movies" if being truly informal) and we don't use cinema in everyday speech at all (that is a big difference from UK English).
Also it is inconsistent as some questions do accept theater for kino in place of either movie theater or cinema. Either all should accept it or all should not.
Well, there are not that many reports, actually ;)
But yes, we gave it another thought and decided to accept "theater" everywhere.