Great Game is a term coined in the 19th century to describe the rivalry between the then imperial powers, Russia and Britain, to gain control of the Central Asian region.
The new game, played between the United States and the post-Communist Russia, has the same objectives, albeit with different players.
The SCO notice to Washington was followed by statements from the Uzbek and Kyrgyz governments suggesting they were reconsidering the future of American bases on their territory.
A day after his victory in the presidential polls on 17 July, Kyrgyz President Kurmanbek Bakiev said the presence of a US base in the Central Asian nation should be reconsidered.
A week earlier, neighbouring Uzbekistan, too, had given warning shots to the US about its presence in this oil-rich country.
"Central Asia is a chessboard for competing interests," says Alexander Neill, head of the Asia Security Programme at the Royal United Services Institute for Defence and Security Studies in London.
"It has huge energy resources, and when you look at China's multilateral engagement, the SCO is clearly something they're concentrating on in order to compete with American interests in the region ... it's a game of energy strategy more than anything else."
Formally created in Shanghai in June 2001 as a security forum to combat terrorism, the SCO's member states include China and Russia, as well as the Central Asian republics of Kyrgyzstan, Tajikistan, Kazakhstan and Uzbekistan.
Since 2001, it has evolved into an economic, energy and security forum.
In a joint declaration, SCO members said:
"As the active military phase in the anti-terror operation in Afghanistan is nearing completion, the SCO would like the coalition's members to decide on the deadline for the use of the temporary infrastructure and for their military contingents' presence in those countries."
America and France have troops based in Uzbekistan, Kyrgyzstan and Tajikistan.
Formerly part of the Soviet Union, Central Asia is seen by Russia and China as their back yard. Ruled by authoritarian leaders who are often criticised by human rights observers, the region is also home to extremist Islamic groups.
The recent American presence, in the form of oil money and troops - while initially welcomed by Central Asian states as part of the "war on terror" and a counter-balance to Russia's own designs on its former provinces - now appears to be under threat.
After last year's "orange revolution" in Ukraine - when president-elect Viktor Yanukovych was forced to step down in the face of popular protests and allegations of electoral fraud - and this year's unrest in Kyrgyzstan, when president Askar Akaev fled the country to Russia, the suspicion is that America is trying to overthrow the area's traditionally dictatorial and pro-Russian leaders.
"In the view of the foreign ministry of Uzbekistan, these considerations should be central to examining the prospects of the future presence of the US military force at the Khanabad air base"
Uzbek government statement
Talking at the conference, Uzbekistan President Islam Karimov suggested that outside forces were at work "to create instability and undermine the region economically in order to impose their own development model".
After a massacre in eastern Uzbekistan in May, when government troops reportedly killed hundreds of protesting civilians, America and other Western countries called for an independent inquiry.
Karimov refused, subsequently curbed America's flying rights from its airbase near the capital of Tashkent and, this month, issued a notice that listed grievances with the way the airbase was being run, including a failure to pay landing and takeoff fees.
Use of the airbase was negotiated after the attacks of 11 September as part of America's invasion of Afghanistan.
Only a week after the massacre, Karimov was being feted in Beijing, his security policies supported, and a $600 million oil and gas joint venture signed.
In recent years, China has been adept at filling the vacuum left by Western companies either forbidden to, or unwilling to, do business in countries that have become international pariahs.
Those countries include Sudan, Zimbabwe, Nepal and Myanmar.
The latest announcement by the SCO appears to be the next move in China's game of chess. Taking advantage of a rise in anti-American sentiment among Central Asian leaders, China, along with Russia, is hoping to woo regional statesmen into signing firmer security and energy deals.
Behind this is not only China's own strategic concerns in keeping Central Asia free of US troops but also China's growing energy needs.
China consumes 5.5 millions barrels of oil a day, 30% of which is imported, and the US Energy Information Administration estimates China's demand will rise to 11 million barrels a day by 2025.
Although the majority of imported oil is shipped on tankers, the ongoing construction of pipelines across China and into Central Asia may soon change this.
"China definitely wants to secure resources now heading west, and divert them to head eastwards," says Neill.
In part, the success of this policy will depend on what the SCO can become. Greeted with some skepticism by Western observers when it began, the organisation has mushroomed. Having taken over the presidency this year, it seems likely that China will press to include Iran, Pakistan, India and Mongolia - four nations granted observer status at the July summit.
"We see the SCO as a possible forum for ironing out differences in Asia,"
Expert on Sino-US relations at Beijing's Foreign Language University
"They don't want to give the impression that the SCO is a home-grown baby ... the Chinese are playing a game to tidy up their international image and will try and create a major movement ... though not necessarily at the expense of creating leverage against ASEAN or APEC," says Neill.
Chinese observers concur. "We see the SCO as a possible forum for ironing out differences in Asia," says Mei Renyi, an expert on Sino-US relations at the Beijing Foreign Language University. "As long as it helps to bring peace and stability in the area, we would like to see the SCO continue. How it develops will depend on how the incorporation of observer nations develop."
One thing is clear - America will not be invited to sit at this table.