Dating sims, raising sims, and other "social simulation" games. Common elements include stat management for the protagonist and turn-based schedule management. The stat systems can resemble other RPGs, but govern interactions beyond combat (or exclude distinct combat phases completely).
If there's titles I've missed, you can reach me at stepnix401(at)gmail(dot)com
Publisher classes it a simulation game on their site, although the ad copy makes it look like a point and click adventure game
Publisher classes it as a dating sim on their site
Third in a series, each gets progressively more complex mechanics until it hits simulation territory
