Hah! Fooled you! This is really a retitled The Mysterious Dr. Fu Manchu, the first American film featuring Sax Rohmer's insidious villain. So why The Red Dragon? This Internet Archive entry shows how obvious the addition of the title on the credits was. The film was relased in many counties, all with a variant of Fu Manchu in the title, except for Italy, where it was released as Il drago rosso. I can't think of any reason why the Italian title would suddenly be tacked onto the American version of the film. Go figure.
Fu Manchu had previously appeared in two British silent movie series with each episode about twenty minutes long: The Mystery of Dr. Fu Manchu (1923, which consited of fifteen episodes) and The Further Mysteries of Fu Manchu (1924, with eight additional episodes), both starring Harry Agar Lyons as Fu Manchu. Twenty-one of these episodes survive, with a twenty-second only in partial form.
Warner Oland, better known for his later portrayal of Charlie Chan in sixteen films (a seventeeth movie, Charlie Chan at the Ringside was unfinished when Oland died of pneumonia in 1938; it was reshot with Peter Lorre and released as Mr. Moto's Gamble.), played Fu Manchu. Unlike the character in the Rohmer novels, this Fu Manchu began as a humnitarian but turned into a killing revenge machine when his wife and child were killed during the Boxer Rebellion in 1900. Two decades later, Fu Manchu has killed everyone he holds responsible for the death of his family except for one man and his offspring, who are now living in England. Fu Manchu's ward, Lia Eltham (played by the lovely Jean Arthur), is an unwilling pawn of Fu Manchu and things get complicate when seh falls in love with one of the intended victims, Dr. Jack Petrie (played by Neil Hamilton). Inspector Nayland Smith, here a Scotland Yard detective (played by O. P. Heggie), discovers the plot and tries to intervene. In the film, Fu Manchu is still a brilliant scientist but has no interest in taking over the world.
An early talkie with all the interesting flaws of that time. And then there's the racism thing...It's easy to say that this was from the culture of the time, but this film will be off-putting for some viewers.
For those who grew up on Fu Manchu back in the days when they were innocent, this movie is a (somewhat creaky) treat.