Right conclusion, wrong reasoning. The convention is to use disc with a C for optical, disk with a K for magnetic, nothing to do with whether the "round" thing is in a casing or not.
It's a convention based on who picked the name. IBM liked it to be spelt with a k, Philips/Sony liked to use c. DVD and bluray carried on the same spelling as CD to avoid confusion, but most people don't even know what DVD stands for so the point is moot. Whatever spelling Nintendo used is correct for the DD.
I doubt they spent as much time picking the name as people have spent making up reasons for why they did (or as long as I spent writing this post).







