“Those indeed were the days, my friend!”

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If the Mamelukes had been able to continue to hold Egypto-Syria while the Mongols conquered (or at least periodically ravaged) Central and Western Europe, it might have led to an eventual Islamic ascendancy, via Mameluke/Arab domination of the Mediterranean, or via the Mongols adopting Islam, (which the Tartar Golden Horde did in Russia).

Alternatively, the Mameluke example might suggest military emulation (or at least parallels) in Europe.
The Polish husaria or “Winged Cavalry” are suggestive: armoured medium cavalry (at least some of whom also carried bows – later firearms) they were organised in units, capable of controlled battlefield maneouvre under control, and one of their major enemies were the Tartars (i.e. Mongols).

What could Venice offer, you might ask? Intelligence, that’s what. Some of the Mongol attacks were based on intelligence about their targets previously gathered by Venetian merchants.

The Mongols were good about honoring alliances if the other side didn’t cross them, and even if they’d overrun western Europe, I don’t believe they would have conquered Venice and the territories it ruled.

As to the military campaigns, I’ve always been in awe of Subatai’s reconnaissance-in-force as possibly the single most brilliant and successful military campaign in history. Subatai was one of the most brilliant military strategists and tacticians in history, and was recognized as such during his lifetime. He was given the singular honor of being permitted to enter the Great Khan’s tent and to seat himself without warning or fanfare or permission, any time he wanted.

Many people don’t know that between WWI and WWII when the Europeans were trying to figure out what to do with tanks, some strategists studied the campaigns of the Mongols and used them as examples.

The Mongols had the only significant army I’ve ever heard of in history which included no infantry. But it’s not the case that they were exclusively cavalry; they often included units of Chinese engineers, who were there to build and operate siege engines.