Intriguing romance, for me, is any romantic novel/story that has an element of intrigue, or any intrigue/crime novel that has an element of romance. Think Alfred Hitchcock's Rebecca and The 39 Steps. Neither are typical romances, yet both have the tropes of both romance and crime combined; Rebecca more so than The 39 Steps, but even the latter film has a romance sewn into the plot.
When I first started writing, I found it very hard to write a 'straight' romance. By straight, I'm not talking about in terms of sexuality. What I mean is a romance that's solely about the hero and heroine and the conflict that keeps them apart with no other sub-plots. So when I first started writing, if a novel stalled, or I felt like banging their heads together, I'd throw in a dead body just to liven things up. Or if I wrote a crime novel, I'd shoehorn a romance in there. The problem was that my novels were neither fish nor fowl, because they hadn't been planned properly.
Only when I sat down to write a true novel of romantic intrigue, The Secret of Helena's Bay, did things fall into place for me and I began to learn how to sew the two separate genres together in a way that was (hopefully) seamless. That was the first romantic intrigue I had published, and I've written loads more since then.
But I've come to realise that any romance, even a straight boy-meets-girl-boy-loses-girl-boy-gets-girl-back is an intrigue of sorts. There's usually some secret in the conflict that keeps them apart. It can be a secret baby, a betrayal, or something that one of them did that they think the other will hate them for. My novel, The Future Mrs Winter (inspired by Rebecca) is as 'straight' as any romance I've ever written, but there's still an element of intrigue in there.
Hence intriguing romance.