> The Mongoles have not redrawn borders along a line on a map the way British and French have, creating the mess we now have in the Middle East.
Back then there was not really the same concept of boarders. But you can be 100% sure that the Mongols picked sides in many local conflicts and simply layed down the law on things like grazing rights and many others things.
> I can't make a complete list of criteria that defines colonialism, but to claim that it was no different than other conquests is to betray complete historical illiteracy.
It really isn't. Sure colonialism from 1800 is not the same as 1200 century mongol conquest. But to draw a line between colonialism and all other types of conquest in human history is actually historically questionable.
Comparing colonialism to other conquests at the same time is very apt. Empires impose institutions and take sides in local conflicts, enforcing new laws making deals with neighbours not to the advantage of locals and so on.
Unless you can lay out a set of clear differences between colonialism and all other froms of one society taking over another, I see no reason to treat collonialism as seperate.
> The entire country India was ruled by a private company
And in other cases, for exmaple the mongol one specific branch of the family was put in command of a region and those families often engadged in trade of the resources from their part of the empire. There are lots and lots of ways empires manage their 'colonies', a quasi private 'company' is certaintly not typical but its also not ahistorical as far as I can see.