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.