Maybe that is why I tend to think of it as a kind of old fashioned word which is rather less used nowadays. It suggests a halfway stage between outright puzzling questions and curious, rather vague, passing fascination with something or other.
When I looked ‘intrigue’ up in the dictionary, I found it can in fact mean a puzzle or questionable scheme. But interestingly it can also mean conspiracy, double dealing, trickery and even, of course an affair. An old fashioned affair/liaison was often called an intrigue.
I think the word could also be used when referring to the questions that a writer poses at the beginning of a stroy to get the reader hooked into the tale. In writing thrillers it is unquestionably the raising of interesting questions and mini puzzles of the ‘will he/won’t he succeed’ variety that make up the entire plot of an 'edge of your seat' thriller. In other words the story must intrigue the reader from start to finish and that intrigue should rise to full on tension as the conflicts escalate and the hero get’s into worse and worse trouble.