Zoomable version:
https://brilliantmaps.com/medieval-trade-routes/

Fine map, good to see the old names. But some of these routes are pretty impassable even today - for example I doubt the Wakhan corridor was ever a major route, even the bottom of that narrow valley rises above 4000m. And note Torugart pass (been there…) is north of Kashgar on the way to Issyk Kul (missing lake), not on the way to Osh. So, considering the mountains, I guess a larger fraction than indicated crossed the steppe further north - horses wouldn’t need roads or cities, but it’s easier.