I wouldn't necessarily say that the State of Palestine is not a real state, but it just isn't a state whose territory includes Gaza under any reasonable interpretation, despite what some international lawyers say. It's unprecedented to say "we deem the actual (sort of) elected government illegitimate, and deem this other entity as the rightful government" when that other entity has never controlled, administered, or been popularly supported in the territory in question.

I'm not sure what you mean about the ICC relying on Israeli claims about Hamas? If the ICC wanted to go after Hamas leaders, aside from the questionable jurisdictional argument, is seems like the easiest case. There's no question that Hamas leaders were involved in taking hostages, for example, which is just one of many war crimes the ICC could prosecute.