I am trying to solve the Rubik's cube in the picture using the layers' method. I used successfully the same algorithm on another cube, but somehow when I reach the last stage it just does not work. Does this configuration look legit (hence, I just need to try harder :) ) to you or is this cube corrupted?
This position is not solvable without twisting a corner, I just tested it on a cube that I have handy.
If you are unable to twist a corner (as that cube doesn't seem like one that would be easy to do that on), you can pop off the caps of each center piece and loosen the screw underneath.
Then, either twist the corners once the cube is looser (though this could be some trial and error), or you could disassemble the whole cube and rebuild it, that way you can ensure that everything is how it belongs.