Think of your own life. Do you now take responsibility for any things or people who weren't in your circle of responsibility when you were younger? Hasn't assuming those responsibilities especially the ones for which you willingly volunteered for made you a deeper person?
This isn't just an accidental phenomenon. Responsibility can promote depth because, to truly take responsibility for another, you must, to a lesser or greater degree, understand that person who they are, their needs, their dreams. You need to expand beyond your own viewpoint and see the world they way they do. This causes depth.
Things can get even more complex. Take a parenting dilemma, for instance: You might see things from your children's point of view, but also see things from your own point of view. That means there might be aspects to the situations they face, or aspects of themselves, that you see clearly but that they don't see at all.
What can turn this broadened insight into a dilemma is when you know that the best thing to do is not intervene in a painful or tough situation they're facing and let them learn for themselves, even when your wisdom could save them misery.
So responsibility doesn't always mean solving someone else's problems. It might mean seeing that what they need is to solve their own problems, even if you love them and it kills you inside to see them suffer, when you could so easily whisk away their pain.
Responsibility makes us expand. We have to be ourselves, but on some level, be another or others as well. Thus, it makes us deeper.
When a game causes us to take responsibility for another, that also gives us depth. By "causes us," I don't mean that a game should force us to take responsibility. In games where it's relevant, I believe it's better to provide incentives for the player to take responsibility for NPCs, for a culture, for a planet, or for something else.
The player can be incentivized to take responsibility for NPCs by using techniques covered in various chapters in this book, such as:
When you play chess, you have responsibility to protect your king. But playing chess doesn't make you a deeper person. First-Person Deepening results from taking responsibility for people, organizations, species, and things that we care about. This is why, for taking responsibility to cause a player to become deeper, the technique requires some of the other Emotioneering techniques to also be used, to bring about caring.