The hunters had bagged about five houbaras a day, a respectable haul, and by Dec. 15, they were almost ready to return home. That night, as the clear desert air turned bitterly cold, the men warmed themselves around bonfires. Servants bustled around them, grilling a lavish supper and pouring steaming glasses of tea. At about 3 a.m., one member of the hunting party, a 37-year-old Al Thani whom I’ll call Abu Mohammed, was awakened by a servant running into his tent. (He spoke to me on the condition that I not reveal his name.) The servant was terrified. Soldiers were all over the camp, he said. Abu Mohammed got up, dressed quickly and then peeked through the slit between the canvas tent’s flaps. He saw men in uniform and dozens of S.U.V.s and trucks mounted with heavy machine guns. At first, he thought it must be a mix-up, or perhaps a visit by the Iraqi military to warn them about some danger. But within a few minutes, men wearing black balaclavas entered his tent. They were armed with AK-47s. One of them held a clipboard and read out a list of names. He seemed to be looking for the most senior member of the Al Thani family. The gunmen led Abu Mohammed outside into the cold desert air. There, in the glare of headlights, he saw his relatives lying face down on the ground in their long white thobes, their hands cuffed behind them. Men were pointing rifles at their backs. In that instant, he felt certain that their captors were ISIS and soon they would all be killed.

Abu Mohammed heard a voice from the walkie-talkies carried by the kidnappers: Leave everything and get out now. He couldn’t place the accent or determine who these men worked for. They hustled the Qataris into S.U.V.s and blindfolded them. The engines gunned, and they roared off into the desert blackness.

As soon as the convoy reached a paved road, the captives were hustled out of the S.U.V.s and pushed into vans. They found themselves on the floor, still handcuffed and blindfolded, lurching painfully against other bound bodies every time the speeding van hit a bump. At some point, one kidnapper turned back toward the hostages and began saying crude and insulting things about Aisha, the third wife of the Prophet Muhammad. In the Arab world, this sort of insult is a dead giveaway. Sunnis revere Aisha, but Shiites revile her as a traitor who fought against Ali, the foundational figure of Shiite tradition. Abu Mohammed and his fellow hostages instantly understood they were in the hands of Shiite militiamen, not ISIS or any other jihadi group.

After three or four hours of driving, the vans stopped. They could hear jets taking off and landing and the sound of soldiers’ voices in unison. But in addition to military orders and salutes, they heard voices chanting “Ya Hussein!” — a Shiite slogan. The captives couldn’t place their location, but they were most likely on the edge of Tallil air base near Nasiriya, one of the largest military installations in southern Iraq. In the strange tug of war that typifies today’s Iraq, the country’s military — trained and supported by the United States — operates literally side by side with Shiite militias backed by Iran. The captives were held on the base for several days, then blindfolded again and driven to a house, where they were locked in basement cells.

At one point, Abu Mohammed — hoping to work this out Qatari-style — pulled out his wallet. (The kidnappers had already taken all their cellphones and tossed them out the windows during the drive.) He had about 120,000 Qatari riyals inside, roughly equivalent to $33,000. “We can pay,” he said. Other hostages had more with them; the total, he said, was probably equal to several hundred thousand dollars, if not more. The lead kidnapper looked unimpressed. “You think we want your money?” he said.

Word of the kidnapping first reached Qatar at about 6 a.m., spreading a chain of panicked phone calls through the government and the royal family. The news underscored the vulnerabilities that have come with Qatar’s sudden rise to prominence. A tiny, thumb-shaped peninsula jutting into the Persian Gulf, Qatar has catapulted from poverty to immense wealth in just the past three decades, thanks to natural-gas deposits under its desert and coastline. It is a country with a G.D.P. of $181 billion but only around 300,000 citizens, about the same size as Pittsburgh. It sits between the region’s great Shiite power — Iran, just across the water — and its most influential Sunni state, Saudi Arabia. Starting in the 1990s, Qatar tried to protect itself by aggressively courting and irritating all sides at once. It made overtures to Syria, Iran and Hezbollah, the region’s rising “Shiite axis,” angering both the Saudis and the United States. At the same time, it also reached out to other Sunni countries, using its endless money to broker diplomatic deals in Lebanon and Yemen. It birthed Al Jazeera, the gadfly satellite channel that pleased crowds with its anti-American broadcasts, even as Qatar continued to host the largest American military base in the Middle East.