I'm guessing you are able to create and work with struct arrays, which is one of the built-in types in MATLAB. I suspect your edit of your question is correct, that the structure_list variable was created as an instance of a user-defined class named structure. If the definition of the structure class was not present when you tried to load it, MATLAB wouldn't know how to interpret the saved data as a structure object.
It would be like trying to turn a kitchen's worth of ingredients (the data in the MAT-file) into a cooked meal (object): easy if you have a recipe (the class definition), perhaps not so easy if you don't.
I reopened this question so that if someone else encounters this same error message in the future they can find the discussion in a search and learn the potential (IMO probable) cause.