That's so weirdly specific, most games have conflict of some sort of other in which the game is centred around resolving, and have at least one male character.
I guess there are all those fan service laden battle games like Senran Kagura but I'm not really familiar with them at all outside their marketing, but from what I've seen the combat looks very cartoonish. There are JRPGs such as Blue Reflection, a game about magical girls... but again I'm not familiar enough to know whether it actually fits your specific wants. There's also Rabi-Ribi, which looks like something I might play myself because it looks like a fun Metroidvania crossed with bullet hell elements. And there's the Hatsune Miku series, which are music rhythm games. The only other thing I can think of that might fit your wants would be harem/dating sim/yuri visual novels. And though I've read a fair amount of visual novels, I can't say I've read many in those genres and none that fit your description, but I know there are absolutely tons out there that would.
The only game I've played that I can think of that fits your description is Huniepop. It's basically just like Puzzle Quest, but instead of each match being a fight with monsters, you're taking a woman on a date.