My understanding is that they didn't need his agreement in the first place, but they voluntarily entered into a contract with Kubrick that gave him the final say on publishing in exchange for him agreeing to be interviewed for the book.
If they didn't need his agreement, but entered into contract anyway that gave so much power. Why? Seems like we are still missing something here. The article didn't get into the legal side.
I said it in my previous comment and it's also in the article. The "why" is so Kubrick would agree to be interviewed for the book. They gave him publishing veto rights that he otherwise wouldn't have had in exchange for that, which is pretty common and typically well worth it.
Contracts to personal affairs not real property, I believe would terminate on his death unless deliberately constructed to use e.g. a trust. I repeat, I'm not a lawyer.
In some economies, Copyright falls to the heirs or assigned owner for a stated period after death. From the University of Melbourne:
Copyright generally lasts 70 years after the death of the creator or after the first year of publication, depending on the type of material and/or when it was first published: Artistic works, including photographs, Dramatic works.
I don't think a contract still stands when one of the party do not exists anymore.
And dead people don't have rights past what they have decided on inheritance and even this can be sometimes overturned by justice. This is the reason wealthy people sometimes give their wealth to a foundation but if the foundation doesn't find a way to make it sustainable and money runs out it also ends up dissolved regardless of the cause it was bound to serve.
Generally, a party has successors that would benefit from the contract.
But without seeing the contract, we don't really know. Perhaps it only bound the original publisher, and not the author, but some other contract had bound the author to only publish through that publisher, and that publication contract is no longer in force. Who knows, the article doesn't tell us.
Dead people have no right to privacy in law as I understand it.
Not a lawyer, not in the economies involved in this.
"it depends"