This is almost trivially refuted by reading a climate map. Traveling along the Silk Road takes you from a Mediterranean climate into a semi-desert alluvial flood plain, into mountains and high steppes, then back into desert, then low steppes, then mountains, then high desert, then more mountains, and then rich alluvial flood plain of East China, without deviating all that much in latitude. Travel north from West Texas, and you start with high altitude steppe, then continue with high altitude steppe until you reach Edmonton. Indeed, looking at a climate map of the Americas, you'll notice that it's pretty much a smooth gradient in latitude.

Now Eurasia does have some similar climatic belts on an east-west axis--namely the tundra, taiga, and steppes of Russia. Which are regions that are not known as being founts of civilization.

Indeed, if you actually look at the history of the Americas versus the history of Eurasia, there's good evidence for transfer of what we might term foundational technologies of civilization along the north-south axis of the Americas (metallurgy, pottery, and most importantly of all, maize), while there's not really any evidence of such transfer between the Mediterranean and Chinese worlds in Eurasia.