Since the US withdrawal from Afghanistan, the world's top diplomats have been beating a path to Qatar, long the gateway to the Taliban and now the essential go-between as the West tries to deal with the new Kabul government. This is no accident.

Analysts describe Qatar's emergence as a broker in Afghanistan as a part of a carefully nurtured strategy by the tiny but rich state to bolster its own security, by becoming indispensable as a venue for international mediation.

The world's biggest liquefied natural gas producer, the small desert peninsula country is one of the wealthiest nations per capita. It is home to barely 3 million people, 85 percent of them foreigners with guest worker visas. Yet it has long held outsized ambitions, hosting both the Middle East's biggest US airbase and its most influential TV channel.

It squandered much of its regional clout over the past decade by...