The definition of "pre-history" as before writing systems is the common use of the term. For example, that is the definition used by dictionary sites and wikipedia. While we can obviously choose to use a different definition from that commonly used, we should only do so if we have a good reason to avoid confusion.
I would also argue that the definition makes sense. The reason why writing is relevant to history is because that is how we know what happened. While old documents rarely attempt to be a (relatively) unbiased statement of facts like more modern history, they do at least provide evidence as to what happened. That is how we know the names of kings, when they went to war and with who and their stated reasons for going to war. For civilizations without writings, we have to rely on archaeological evidence. That can tell us more or less what happened, but it leaves huge questions as to why. While documents can be misleading (either accidentally or intentionally), they still give us huge amounts of information. The Illiad is a terrible history book, but it provides huge amounts of information about the people who wrote it; what they believed and what they thought was important. That sort of insight is entirely missing from our knowledge of pre-historic societies.