Why even atheists need the Hypothetical Supreme Authority that is the Abrahamic God to settle their disputes

Because it is morally and intellectually necessary to do so.

Atheists do this every time they have a dispute with each other and appeal to a higher authority to decide who wins.

If this were a legal dispute, it would go to the Supreme Court. If they were still not happy, one of them would be invoking some hypothetical entity with more justice than the Supreme Court, whether or not he believed in God.

Let us imagine that this court higher than the Supreme Court of his country could be set up, and he was still not happy with the decision with the International Supreme Court.

If he were still not happy, he would be going higher and higher until he got to God Himself, even if he insisted on calling the Abrahamic God "a Hypothetical Supreme Being".

And so I have demonstrated the logical necessity of the Abrahamic God for atheists.