Quote from ChimerayIsn't level design just a subgenre of game design to begin with? At least that's how I always viewed it, often you find yourself designing game systems next to your level design duties. But I suppose that depends from studio to studio.
It does seem quite studio dependant. I've got friends at other studios where game designer and level designer are the same thing and then look at somewhere like Codemasters and Level Designers and Games Designers are quite separate. On top of that you have Quest/Mission designers too though.
I'd still be happy to class them all as Game Design though personally.