we have so many mini genre's these days like Castle / Tower Defense, Casual Match 3, etc. Is there a name for the category that these games fall under? 'Doodle Jump' 'Air Bear' 'Papi Jump' 'SpringFling' 'Guttu Jump' 'Leaf Bound' 'Scarecrow' I'm sure there are more I am leaving out. It's a genre I am actually growing to like a lot (I thought it was boring when it was just 'Papi Jump', but 'SpringFling' and 'Doodlejump' really bring it to life.
I'd guess they all fall vaguely under platformer and then drill down from there. In SpringFling's case it probably goes: Platformer --> Vertical Platformer ------> Physics based vertical platformer
That's what I'd go with. You can add Rock Climber to that list. Earliest game I can think of that plays like this was Climber Game & Watch: I like this one better than Ice Climber (NES) because it's just jumping up and up and up...