Although I am a big fan of action-adventure games with good stories, twin-stick shooting is my least favorite mechanic in video games, as well as my most least experienced genre. One twin-stick game I did enjoy was Nuclear Throne.
I generally enjoy games that tell stories in different ways. There is no particular game in my gaming history that is close to this, but one game that I liked that told a story in a unique way was Her Story.
I enjoy playing platformers, especially platformers with a good story progression and solid controls. Ori and the Blind Forest is my favorite most recently played platformer that combines both story and game mechanics into a good gaming experience.
The only game I’ve played that I can think of that is remotely close to what Newt One does is Journey (PS3). I personally found Journey to be a very pleasant experience and Newt One taps into similar feelings.