His publishers might have cause to be annoyed if they have a contract for more books, but the readers, however disappointed, don't have a moral right to dictate a writer's future labour. And that's what writing novels is—it's work for money, like programming or plumbing, not some mystical calling or vocation.
But they are entitled to feel cheated, and loudly proclaim that they were cheated. Especially with a story as full of intrigue as A Song of Ice and Fire.
By comparison, fans of Agatha Christie's work would not have any entitlement to complain if she stopped after three novels, as those novels were complete works in and of themselves. But they would have every reason to complain if she published the first half of And Then There Were None, but never published the ending.
Of course they would.
Note that I'm not saying some fans wouldn't have been pressuring her into writing more if she had stopped. I'm saying those fans, unlike the ASOIAF fandom, wouldn't have a leg to stand on.
That's completely irrelevant. Everyone is entitled to feel however they feel and think whatever they think and should not be precluded from voicing their opinions. Why should your opinion of the relative completeness of one story versus another determine whether someone else is permitted to express disappointment with a story?
My contention is that George RR Martin is cheating his ASOIAF readers by spending time on other works instead of writing the next ASOIAF novel.
By contrast, I don't think Agatha Christie would have been cheating her Poirot fans in any way by writing Miss Marple novels instead of Poirot ones.
The reason I draw this difference is that you can enjoy (or hate) any particular Poirot book individually. By contrast, you can't really like A Dance With Dragons without knowing if what happens next to some of those characters actually resolves the tension and mystery in a satisfying way (or doesn't resolve it, but in a satisfying meaningful way, like a good open ending).
Every story has details not followed up on. Just like real life.
LOST had an ending but it was terrible because the story kept piling on more bullshit.
GOT TV had an ending and it was terrible.
ASOIAF is a short chronicle (yet still full of many great characterizations, episodes, and plot lines) of characters coming and going through the world. Some plot lines start in the middle, some end in the middle, because neither us nor GRRM are immortal beings.
A lot of them wouldn't have bought the books if they knew there will never be a conclusion.
I agree with your overall comment, but this is not entirely true. For many writers, writing is a vocation. They would do it even if they couldn't make a living out of it, just like a painter would paint even if nobody commissioned any of their work.
It just happens that for a relatively small percentage of writers, writing is a viable way to make enough money to make a living.
Do this day, 12 years after this was written, he blogs about how the books are his top priority. He is certainly giving his readers the idea that he owes them a finish by constantly communicating that he will finish.
No, but HBO did, he (co?)wrote Fire and Blood to give them material for a new GoT style TV show; they probably paid him so much to cram its writing in between the mainline ASoIaF books. On top of the licenses for the once popular TV show.