The term “Great Game” refers to the period 1800-1900 and the confrontation between Great Britain and the Russian Empire in Central Asia.
Great Britain was the greatest naval power of the time, and through the tropical zones of India, which was their colony, they British were getting cotton, tea etc, all very important to their economy. Remember that the British made the Industrial Revolution in the previous century.
The Russians could not match the British as a naval power, but they were using the local populations to attack Britain in India. At the same time Russia was gaining more and more influence in Central Asia, approaching India, the most important British colony. At the time Pakistan was the Muslim part of India.
The British-Russian rivalry was mainly taking place in Afghanistan and Iran, and it was about railways and not about oil and natural gas pipelines. Oil rose as the greatest geopolitical factor in the 20th Century or maybe a bit earlier.
The British and the Russians temporarily put aside their difference in 1907 in order to fight the Germans and the Turks in the First World War (1914-1918)
A sequel of the Great Game took place in 1979, when the Soviets invaded Afghanistan, but this time it was the Americans who were fighting the Soviets in order to protect the Persian Gulf, this time with the help of the Arabs and the Pakistanis.
After the collapse of the Soviet Union in 1991, the Muslim colonies of Russia in Central Asia became independent Communist dictatorships, and the New Great Game begun.
The Americans were trying to send the oil and gas of Central Asia to Europe, through Turkey, and to the Indian Ocean, through Afghanistan, in order for Central Asia not to be dependent on their rivals (Russia, China, Iran).
The Chinese were heavily investing in these countries, while avoiding to establish a militarily presence, in order not to upset Russia, and not to cause problems in their Muslim province of Xin Jiang. China was absorbing the oil and gas of Central Asia, becoming the dominant economic power. Soon China will be the dominant militarily power too in Central Asia.
India is desperately trying to antagonize China in Central Asia, but she is blocked by Pakistan. If India was to win the disputed are of Kashmir, she would open a corridor to Afghanistan avoiding Pakistan.
The Russians were trying to remain the main military power of Central Asia, and at the same time block the oil and gas of the region to reach Europe and hurt their own exports. At the same time they were trying to use these countries to export oil and gas to South Asia, which was a new market for them.
The Arabs and the Iranians were trying to antagonize Russia in Central Asia, and with the use of Al Qaeda and the Taliban they were trying to block the oil and natural gas of the region from reaching the Indian Ocean, something that would hurt their own exports.
Turkey saw a great opportunity of reviving Pan-Turkism, i.e. of establishing a union of Turkic countries from East Mediterranean Sea (Turkey) to the Muslim Chinese province of Xin Jiang. That would make Turkey a super power with huge oil and natural gas reserves.