Hi Sasha,
Let's start from the definition of both words. "Tributaries" are smaller streams or rivers that will flow into larger streams or rivers. For example, the Dnieper is a famous river that flows through Ukraine, and Supiy is one of its tributaries.
"tributaries" in your sentence is used metaphorically to refer to the main route that comes to mind when people talk about the Old Silk Road as well as minor routes that branch off from the main route or converge again with the main route. Therefore, this is not a watery tributary, instead, it is a network of land routes.
Moving on, "storied" is an adjective to refer to something that is historically significant and is often spoken or written about. In your sentence, it means that the network of land routes are historic and are often mentioned or advertised.
*Just as a side discussion, verbs that end with "ed", "ing" and "en" can function as adjectives (adj) instead. Examples: We are bored (adj) as the lecturer is boring (adj). Such adjectives are called participle adjectives as they are formed using past participles and present participles.
The last part of your sentence describes many tourism-related businesses that have sprung up along the main Old Silk Road as well as its "tributaries" of minor roads. These businesses (hotels, restaurants and souvenir shops) capitalise on the fact that tourists often associate Polo's name with the Old Silk Road, and they use Polo's name to their advantage and draw business from tourists.
I hope this explanation helps you.