Not required. Every quest is generated complete and written in full without a key: the title, the read-aloud text, the DM notes and every NPC's line are procedural and reproduce from the seed. A key only lets a language model rewrite those words, field by field; anything it does not return keeps the sentence the generator wrote, and no number in the quest changes either way.
The key is stored in this browser's local storage, is sent only to api.openai.com, and is never written into a quest link or a saved file.