First off, yeah, people seem to be forgetting about Catherine, which is a successful game about relationships (and box pushing puzzles... mmm... makes me want to replay it).
Ahem. Anyway.
But yes, why not? I don't see why everyone keeps jumping to sex or thinking of Visual novels. Here, let me suggest a Romance game for you:
Don Juan, the Game.
What are the mechanics? Well, you are Don Juan, the Italian Libertine. Your gameplay is an Assassins Creed 2 Clone - you run around Italian cities, climbing on buildings and sneaking about trying to avoid detection. The game is heavily stealth based, but you can fight off guards if necessary, and there are places to hide to avoid pursuers.
What makes it different from Assassins Creed? Well, you aren't trying to assassinate anyone - you're pursuing a main romantic plotline while at the same time accomplishing various story missions. Some of these might include duels (rather than assassinations), but others involve seductions. In the seductions, you are given dialogue options and some sort of sensor that allows you to judge the target's emotional state (ripped off of Deus Ex Human Revolution). You then attempt to seduce them. Success results in some PG-13 sex (make out, fade to black) and then some sort of plot benefit or accomplishment. Maybe seducing the tavern owner's wife allows you to cheat at cards, making winning an important plot card game easier. If you screw up the seduction, you either don't get the benefit or, if you fail badly enough, you might get chased off by her husband and fail the mission.
You have various story and side missions, but aside from the random, the Witcher style sex with various women, you also have the plot, which is a main romantic story line. This, being the main plot, would need to be well written, so you'd probably want to hire some good writers for this part, cause if this writing sucks, then the whole plot is going to suck.
Of course, if you just like climbing about on Italian buildings, you'll probably like the game anyway (particularly since Assassin Creed 3 is ditching Europe and it's awesome architecture).
So there you go - a design document (sort of) for a romance themed game. It's not that hard, guys. Yeesh.
Edit: Corrected a typo and added some bolding and italics to draw attention to the main points.
Edit 2: I'm kind of tempted to make this it's own thread. The more I think about it, the more I think this is a great idea that needs to be made by someone.
tl;dr: Romance games don't need to be dating sims - they can be Assassins Creed 2 clones.
