We've traditionally taken a fairly expansive view of what's on topic here. Essentially, if its about stuff involving humans in the past, where there isn't a better stack for it (eg: Politics, English, etc.)
From a technical sense, yes it is true that anything that isn't relying on written records is not "History", but rather some other discipline.
However, I have two basic issues with limiting our scope that far. The first is practical. For example, there's no Anthropology stack right now to direct people to, so closing anthropology questions just for being anthropology helps nobody. The poor user doesn't get their question answered, and this beta stack has one less question it could sorely use. Perhaps when we make it to "release" it would make sense to break anthropological questions off into their own stack, but for now one stack covering both seems to be plenty.
The other is more philosophical. When you get into ancient history, records are nice to have, but we don't have nearly as much as we'd like. It is only sensible to use archeological finds, linguistic studies, DNA etc. both to fill in the gaps, and to check (or perhaps in cases even correct) the written record. Not doing so, simply because those are other disciplines, would be bad science.
You could then argue, "Well yeah, but once there flat out is no record, surely that's no longer History!" Perhaps technically yes. But I don't see drawing the line at 100% reliance on non-written information to be any less arbitrary than drawing it at 99%, or 80%.
What we are really interested in here is the story of Humanity, as well as we can figure it out scientifically.