Doris Lessing was one of my fave writers going into my twenties, and I completely agree with that last line of the quote.
As to who I write for– I write the first draft primarily for myself, sometimes even the second or the third. But the later drafts almost always have a reader in mind. Not all readers, but one reader, someone I know or imagine, the kind of person who would be interested in such a story.
Sometimes my ideal reader is my betta fish!
What about you? Who do You write for?