The place where games fall shortest is how they handle relationships.
Putting aside fully scripted relationships, there are a lot of games where relationships are part of the gameplay. For example, getting team mates to like you or performing loyalty missions or giving a cartoon cat a comfy chair.
The problem with all of these approaches is that the relationship is a gating mechanism. You move through the relationship to get the reward, whether it's stats or a cut scene or whatever. In turn, the interactions are all rather stilted and transparent. It's made considerably worse because the relationships are not very interesting to move through - you use a variety of extremely basic dialog options or gifts.
Basically, the relationships suck because they're so transparent and flat.
One option to make relationships more interesting is to accept their "level-like" nature. If you're going to move through a relationship, set it up the same way that you might set up a level in a platforming game. Let the player move through its complexities using a more open-ended method of interacting. Fill it with interesting challenges and moments of beauty or terror as things unfold.
The other option is to stop treating relationships like levels. Instead of "using dialog to move through a relationship", you "use relationships to move through dialog". Or whatever else you want to move through. The point is that instead of being equivalent to the level, the relationship is now equivalent to the act of jumping, moving, shooting, building - whatever actions you would take in another game. Instead of being content to burn through, relationships are actions you take to burn through content.
As the most basic example, if you play a father or mother that's going to have a rough week at work, you might spend a few hours playing around with your kids. That'll relax you and give you the determination you need to push through the week.
While your relationship with the kids might change slightly because you spend time with them, the point would be to navigate the challenges of your life by spending time with people. Whether this is an emotional benefit or whether they actually help you with your problems directly, the relationship is largely a stable object, like shooting a gun in a first person shooter. You might change guns, or run out of ammo, or use alt-fire, or it might overheat - there's lots of ways to add complexity, but fundamentally you can rely on a gun to do what it is obviously intended to do.
Anyway, I think both options are interesting. The real issue here is in the objective. Why do you relationship? Whether the relationship is action or terrain, there has to be some reason to play. Hm!