Patrick Dwayne Murphy might evade execution for a brutal murder simply because he chose to mutilate a man on American Indian land instead of on plain old Oklahoma dirt.

But the case has broader implications than Murphy’s fate—among them tribal sovereignty and Western business interests like the oil and gas industry, which is worried about more regulation, taxes, and litigation if the U.S. Supreme Court deems large swaths of the state to be tribal land.

Such a ruling could plunge the state “into civil, criminal, and regulatory turmoil and overturn 111 years of Oklahoma history,” the state warned ahead of...