Feel free to suggest your own themes and genres followed with an explanation.
Genres:
-Platforming: The game even makes a reference about Donkey Kong, which is a platforming game! It was also one of the first genres to be made into video games and yet there is no platforming genre.
-Survival: Many themes in the game can be fitting with the Survival Genre such as Horror, Wild West, Sci-Fi (System Shock), Life and some more, and in Multi Genre it can very well fit with RPG, Action or Adventure i would assume.
Themes:
-Puzzle: I think this fits more as a theme.
Adventure Puzzle = Point and Click style of game
RPG Puzzle = A Lufia II style of game
Casual Puzzle = There are lots of those in App Stores