Many of those countries were part of the Ottoman Empire (between the 13th and 16th centuries) and were thus strongly influenced by the Mughals, originally fromIndia, who brought with them a pervasive Muslim influence, tempered by the artistic traditions of Hinduism, Jainism, and Buddhism.
The TAPI plan, to bring gas from Turkmenistan through Afghanistan and Pakistan into India, would keep Iran out and diminish Russian influence in Central Asia.