Who knows what evil lurks in the hearts of men? Sometimes I do, and in the hearts of the screenwriters for Hollywood, that evil is called "producing inane screenplays for the sake money". But I digress.
Lamont Cranston is a rich playboy. When trouble arises, he is also the Shadow, who has the power to cloud the minds of criminals and thus defeat them. Shiwan Kahn is a descendent of Genghis Khan, who is back again (right in the middle of NY) to resume his conquest of the world. While Shiwan Kahn makes himself comfortable in a palace right in the middle of Manhattan, the Shadow goes about trying to stop him achieving world domination. Since they are both of equal power, having been instructed by the same Oriental school, it should have made for a great showdown. But it does not.
The movie is based on the radio series of the same name, where Orson Welles was the first voice of The Shadow. I have never heard the radio show personally, but from all accounts I've read, there is no justice done. Perhaps the screenwriters wish they had the powers of The Shadow.