Base your storage off of the way you hold your data, not the other way around. Feel me?
If you have something like Minecraft, were you basically have large memory chunks you want to quickly read&write to storage.
Perhaps a memory mapped file
is something for you.
But that is for tile information and like. Perhaps for your entities (characters, items, whatever) you would still opt for a db.
Finally, as others mentioned, you have to be aware of size.
Postgres is a great db, but it consumes a lot of space and is not very portable.
H2 and sqlite on the other hand are.
So try to figure out first what you need in every aspect (what has to be stored, how much space do you have, are you running on a client or is there a server, etc pp) and then find something that fulfils those needs.