I don't think more data than fits in memory is a requirement. An important innovation in databases has been the realization that there are important performance

I don't think more data than fits in memory is a requirement. An important innovation in databases has been the realization that there are important performance benefits from assuming all data can fit in memory even if you still provide persistence. Even persistence isn't really required. A pure analytics view of another database is still a database by itself, but it doesn't need to actually persist anything. It seems like querying is more important to the concept of a database rather than actual storage.