The Silk Road's overland routes operated in parallel with the maritime routes. AlexP is overstating the facts when he says that the overland route was a backup solution for the maritime route. A better answer is that the overland route was strongest in times when there was a strong civilization in Central Asia to push it.
Central Asia had a series of kingdoms and empires through history and was occasionally one of the most advanced parts of the world. Specifically, during the period after the fall of the Tang in China and the decline of the Abbasid Caliphate in Mesopotamia, Central Asia could be considered the most intellectually advanced part of Earth. The combination of Persian scholars, Turkish warriors, Sogdian merchants and Arab religion made it the center of the world, as the riches of China, India, and the Middle East all poured in to trade. Many of the most famous scholars of the Islamic Middle Ages were from Central Asia, such as al-Khwarizmi, after whom algebra was named, and Avicenna, who introduced Indian decimals and Galen's anatomy to the West.
If Central Asia was rich and strong, then the overland route was worthwhile. Such was the case in the Middle Ages, from after the Arab Conquest ~800AD to the decline of the Timurids ~1450 AD. At other periods of time, there were rich cities in Central Asia, and during those times too, trade flourished. The Sogdian city states were rich from ~1AD to ~400AD when the Hepthalites and Turks invaded. This corresponded to the first trade and contacts between Han China and Rome.
If Central Asia is weak, as it appears in your alternate time line, then there is little incentive to trade there, and goods will likely not pass through. On the other hand, if India is rich, then goods will move by sea from China and Indonesia in the East, and Arabia and Persia in the West. This will make India the focus of international trade and cause the 'Silk Road' to pass by sea. This situation happened many times in history too, and was more common than a rich and powerful Central Asia. India was rich as far back as the Harappan Era (~2500-1700 BC) then after the Vedic invasion there was much commerce again in the Greco-Roman era (~200 BC-200 AD). After the Islamic invasion there was a great increase in wealth in India that persisted to the present (~1000AD to now).
In conclusion, the trade goes to where the rich middle-man is. Generally speaking, India has been richer than Central Asia, so trade went there. In your world, this is how it would be.