What is your distinction? Is mongodb a database? What about leveldb?
Whether we want it to be so or not the term database is much more encompassing thank it used to be. You can try to fight that change if you want to but it means you'll be speaking a different language that most of the rest of us as a result.
I would draw the line at semantic indexing. If the data is only accessible through immediate metadata (filename, sequence number, datetime, etc) then it's just a data_store_. If the engine also maintains indexes derived from the data being stored, then it's a data_base_. In that regard, Kakfa would not be a database since it has no knowledge of what it is storing.
Honestly, where I'd draw the distinction between a database and a datastore is the ability to do multi-statement transactions.
So, a filesystem? A datastore. Some support fsync on a single file, but multi-file sync isn't usually supported.
MongoDB and LevelDB both support transactions, so I'd err on calling them databases myself.
You're using the term "traditional database" two levels up. Whatever your definition of that is, it's their definition of "database".
Your initial post says "I have a different definition of 'database'", which is different than anyone else's, as you acknowledge when you refer to that common definition as a 'traditional database'.
Then, you fault them for making an argument that is invalid for your non-standard definition of a database!
No my post said that the term database has evolved beyond their definition. If you want to fight that trend then you will be swimming against the current.