If you haven't seen it, Alfred Hitchcock adapted some of Maugham's stories into a film called, confusingly, Secret Agent* starring John Gielgud as Ashenden, with Madeleine Carroll and Peter Lorre as the Hairless Mexican (who, as you can see below, is neither hairless nor a Mexican in this version!). It loses some of the restraint of Maugham's stories and goes for both suspense and action, which might help with adapting the stories to a game format.
There was also a BBC TV series in the early 1990s, but I haven't seen that.
* Confusingly because he then made a film of Joseph Conrad's novel, The Secret Agent, which he had to call Sabotage. And then he made another film called Saboteur. Oh, Hitch, stop messing with our heads!