English is not my mother tongue, so I might be wrong here, but wouldn't "Smoking not allowed in the café" (w/out the "is" be a totally reasonable phrasing on a sign on the wall, and hence an accptable translation of this sentence?
Instead of thinking the way it should be said the way it is actually said is right there in front of you "smoking is not allowed in the cafe" certain languages use grammar differently and have differentiating sentences.
The audio is strange a little. I am confused. When I hear just the word кафе, the pronunciation seems right to me. There is the э sound at the end of the word. But when listening to the whole sentence, I hear the е sound at the end of the кафе. That's weird.