I’m currently playing The Witcher 3 and I thought it had some fairly unorthodox quests, though I guess on closer examination the “kill, fetch, escort, and collect” aspects were just better disguised . Perhaps it did so by focusing more on the people involved than the quest objective itself, which often took a back seat in favour of exceptional characters and circumstances.
In my opinion, games that deviate from this quaternity usually turn out to be RPGs in name only. Unrest is one such “narrative RPG” I played not so long ago.
And, for purely technical limitations, my own small contribution to the world of video games falls into the same category.