Just for what it's worth, I'm 38 and lived inTexas my whole life and I have never heard anyone say "I am going to the theater" refering to a movie theater. it's always been "going to the movies", " going to the movie theater" or "going to the cinema". If nothing else it goes to show how different coloquial terms can be, and I think DL is right to accept only the most universal forms.
I see a lot of comments about who says theater versus who says cinema and the like. I think the point that isn't being made clearly is that unless you are in the extremely rare circumstance in modern life where you are going to watch a play or an opera, when someone says the word theater, it's just known that the person saying theater means a place that projects movies on a screen to a room of people. In fact, the only times I have heard anyone say theater and NOT mean movie theater, they instinctively added "to watch a play" to make it understood what they meant. No one regularly says theater and means anything but movie theater unless it's part of their job, and/or it is common for them to not see movies. DL is trying to teach us the meaning of the Russian, but if that is to be successful, I feel they should put just as much effort toward the clarity of the English portion of the lessons as well.