The US corporate media is in a panic about declining American power. The list-loving business magazine Forbes – whose slogan is "the capitalist tool" – has named Vladimir Putin the world's most powerful person. Barack Obama, leader of the self-proclaimed "greatest nation on earth", has been demoted to a humiliating number two.

The downgrade seems to be punishment for the US president's flip-flopping over Syria and the Republican-orchestrated government debt ceiling shutdown. But it also reflects US elite breast-beating about economic failure, the rise of China and a loss of global swagger since the Bush years. The likes of Forbes are delighted to have the chance to brand Obama a lame duck.

David Cameron should consider himself lucky to have made it to number 11 – even if that's below Michael Duke, the chief executive of Wal-Mart, and King Abdullah of Saudi Arabia. But the idea that Putin is now more powerful than Obama – or Russia than the US – is beyond absurd.

It's true that Putin – or rather his foreign minister Sergei Lavrov – played a blinder in September by seizing the initiative on Syria and turning the threat of a US attack on Damascus into a UN agreement on chemical weapons. That has made the outright collapse of Russia's Syrian ally less likely. And yes, he cocked a snook at the US by giving asylum to the NSA whistleblower Edward Snowden.

Far more importantly, in the past decade the US suffered a strategic defeat in Iraq and Afghanistan, demonstrating the limits of US power to impose its will on people prepared to fight back. Combined with the crash of 2008, which accelerated relative western decline, that marked the end of the unipolar world. But all that happened under George Bush – and was symbolised by Putin's successful defiance of US threats in the Russian-Georgian war more than five years ago.

Bush may have destroyed the myth of invincibility of the world's first truly global empire – but empire it remains. The US continues to be overwhelmingly the most powerful state in the world, militarily and economically. Its "defence" spending is larger than that of the next dozen states combined. It has bases and forces stationed in a majority of countries of the world – and continues to use them without restraint, from Libya to Pakistan. By contrast, Russia has one military facility outside the former Soviet Union, in Syria.

A New York Times interview with Obama's national security adviser Susan Rice last week has fed the idea that the US is somehow withdrawing from the Middle East as part of its "pivot" to Asia. It isn't. The administration is instead focusing its interventions more directly on Israel, Iran and Syria. Its network of Gulf military bases is in fact being strengthened.

The past 10 years have seen crucial global shifts which will certainly shape this century: the end of the US new world order, the crisis of the western economic model, the breakneck development of China and the progressive tide in Latin America. But none of that should blind us to the reality of continued US global dominance – or confuse the sway of the US president with the leader of a resurgent regional power.