I wouldn't say that "where" is incorrect but only vague. As a teacher or editor, I think I'd revise it as follows:
1) He was supposed to write a short story, but not like this, not one in which one has to know a lot of history to understand what the story is about.
2) You're supposed to write a short story, but not a complicated one, not one in which the writer has to be an expert in history.
I prefer (2) because in (1) "not like this" refers to the manner, not the subject-matter of writing, and as a result "one in which" might sound a little disconnected from its antecedent, which is "a short story."