No, he does not. There is no contract, there is no reliance theory, there is nothing of the sort involved. It is a pure retail transaction and absolutely nothing else. The only way it could be anything else is if you somehow paid for ADWD, TWoW and ADoS ahead of time and never got them. This has not happened.

A product was produced. You bought that product. You bought that product knowing that a meteor could flatten the producer's house tomorrow and you would never get the next part. You bought that product knowing (or fully capable of finding out) that it was part of a series of products that was as yet incomplete. You chose to get invested in the series before it was completed, in a genre littered with examples of series that were never finished, or spiralled out of control and took five times as long to complete as it should have done.

This is a genre where you can have the most reliable, regular author in the world who releases a book every year for years on end, and then suddenly they're taking three years per book (Rowling, Jordan, Donaldson). You can have a very reliable and fast writer who suddenly gives up on the series halfway through for absolutely no discernable reason (Gerrold), or due to family issues (Rawn). You can have a brilliant series which simply doesn't sell, so the next book is cancelled and you're left high and dry (Kearney).

When you buy a book, regardless of if is labelled as Book 4 of 7, the only guarantee you have is that you have is that you have bought that book. The next book might never come out.

If you don't want to be in that position, then you should have waited until the series was completed before buying it.