Well, no one ever said this sort of stuff has to make sense. But, again, what would be the attraction for readers in the 21st Century?
For me, the Fu Manchu books were something of a mirror to another contemporary series of British adventures, Sapper's Bulldog Drummond stories. Both series were typical of their times with independent adventurers taking on criminal masterminds who used more or less the same devices to get their way—hypnotism, poisonous spiders and snakes, new explosives, concealed knives and darts, and alluring dragon ladies. In the better Drummond books, the cast of heroes is entertaining as Bulldog and his gang are full of energetic vim and devil-may-care vigor. Their opponents were, even then, rather two-dimensional cookie-cutter schemers.
On the other side of the glass, readers are fascinated by Fu Manchu, even if his physical presence is limited. Unlike Drummond's boisterous crew, Nayland Smith and Petrie are clearly copied from Conan Doyle. The gullible Greville and the others are manipulated and maneuvered by what Manchu does rather than initiate any action of their own.
So it's the figure of Oriental evil, then, that must be the draw: “tall, lean,
and feline, high-shouldered, with a brow like Shakespeare and a face like Satan, a close-shaven skull, and long, magnetic eyes of the true cat-green.” Never forget that Fu Manchu is a gentleman in the early 20th Century meaning of the term. At the end of Mask, where other villains would have vengeance on their minds, Fu Manchu sends Greville an expensive wedding present. Clearly, Fu and the gang will return to fight another day.
As mentioned before, The Mask of Fu Manchu is probably not the best first novel for new readers, but I'm not qualified to suggest which one would be. Perhaps Daughter? That one remains in my memory from long ago when I thought Rohmer was blending Conan Doyle and John Buchan. Me, I'd stick to those writers, throw in some Sapper, and not spend a lot of time with Fu Manchu. I'm in the mood to re-read Dr. No—lewd is more fun than crude.