I absolutely love games like this. Heavy Rain, Beyond Two Souls, and Detroit Become Human are all fantastic games that really push the boundaries of human emotions through story telling. The choices you make reflect back onto the character.
The telltale games are like this as well, the walking dead game is a master piece in itself even if you don't like zombies. The batman games are great if you love the comics and really lets you feel like batman. The borderlands ones are OK, the first one is the only one I played, and ties into BL4. the second comes from a different studio and has so so reviews. Avoid the expanse... the most boring and out of touch game of them all and was really disappointed with the lack of actual story, it's all very streamlined with the choices more black and white vs shades of Grey.
This leads me into the Dark Pictures anthology. I don't tend to like horror based games but the way these games tell stories are top notch and I believe the only ones you can play with another person, all of these games are phenomenal.
Then theres the wolf among us, that game is amazing at turning a graphic novel based on fairytales into a emotion filled adventure.( The second should be coming out soon but I'm hoping they don't ruin it with MTX).
Last but not least, the guardians of the galaxy game, while not exactly like these has a very similar conversation tool that some of your choices impact the story of the game, but the game play is more focused on fighting and solving puzzles versus just the story itself.
If anyone else knows more games that I'm missing let me know