This is how people should play this kind of games. You dont get "stuck" in walls, that that is the gameplay, there is no stairs here. Just jump again while holding A/D (depending on the direction). Look:
The first example use two walls to climb. The second example is more complex way (just for veterans on Ninja Gaiden).
Give it a try: "stuck" in a wall and hold A or D, and then jump. Just need practice, but when you get it, stuffs like this happen: 