As a gamer that grew up in the 1990s, platformers like this always warm my heart because of the greater focus on gameplay. I also enjoy playing platformers that try to shake things up in one way or another.
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.