Translation:The red square has two shopping malls.
Since it is hard to imagine a square that is actually the color red, it is only natural to assume that the sentence refers to a square that is named "Red Square" in which case "the" is most likely to be omitted in American speech.
Whether "shopping mall" is a traditionally correct use of the word or not, I cannot say, but the word is a valid word in English, British or otherwise. You can blame the Americans for the usage but not the word. BTW, we traditionally use mall for broad, open public space, e. g., "The Mall" in Washington, D. C., which is the open area between the Capitol and the Washington Monument-- not a shabby place at all. "Shopping mall" is more pretentious than ugly.