Some problems immediately arise:
1) Mongol tactics are suited to a world before the absolute dominance of air superiority. You can adapt them, but that would involve the Neo-Khanate using its air force as the equivalent of cavalry, which (if successfully done) quickly negates the OTL deficiences of the Mongols. (Such as not having a good navy, and thus failing utterly when trying to take Japan. A Neo-Khanate with a super-charged air force would quickly lay waste to Japan...)
2) Mongol tactics are suited to a world before long-range missiles. Again, we can have the Neo-Khanate develop the mostest and bestest long-range missiles ever, these being the equivalent of their unsurpassed and long-ranging archery. But again, the scale involved here means that instead of a battle-winning advantage, this gives them a world-conquering advantage.
3) Mongol tactics are suited to a world before atomic weaponry. The fact is that if the Neo-Khanate as suggested in the points aove does arise, the response is nuclear. Even if the Neo-Mongols also have nukes, they can't prevent their enemies from launching. The fact is that the very existence of a conquest-bent Neo-Khanate would prompt the ultima ratio regis to be deployed against them. The scenario therefore must presuppose that an effective counter to nukes has been invented, or that instead of 'early 21st century', we're willing to say 'early 20th century'. (The first option leads to the already suggested outcome of the Neo-Khanate going world-conquering, and the second option... well....
...The thing is: the closest we actually ever got to a Neo-Khanate was Nazi Germany. It was a warped parody, to be sure, but the Blitzkrieg was basically their attempt at it. They had crack troops, they had some excellent weaponry, they had (for a time) the missile advantage, and they had a doctrine of speed that allowed them to overwhelm their enemies. They didn't have the numbers (of everything) and they didn't have the clear-headed leadership.
If you imagine some ASB scenario where Russia has a fascist coup instead of a commie one, and Germany and Russia somehow united to form a single "Eurasian Empire", then they have the numbers (of men, food, raw materials...) required. They'd have the means to build the most planes and the best planes, and to build hundreds of times as many missiles as Germany could in OTL. If they then adopt the same tactics as WWII Germany, minus the Holocaust lunacy... well, then they conquer the world. That's roughly what a Neo-Khanate would look like.
Since the first half of the 20th century, air superiority has only become more important. It can be argued that the failure of the Luftwaffe was one critical weakness for the Nazis already. The closer we get to the present, the more critical this point becomes. A 'present-day' Neo-Khanate, therefore, relies on the following points:
-- Effective neutralisation of strategic nuclear weapons as a tool of force.
-- Overwhelming air superiority; planes of all types superior to anything their enemies have. Best pilots on Earth, trained for this purpose from a very young age, in a staggeringly thorough training programme that weeds out anyone who isn't an ace.
-- Overwhelming missile superiority. Best, fastest, longest-ranging weaponry on Earth. Missiles capable of striking any place on Earth, capable of (more often than not) outspeeding any defence mechanisms that may be attempted.
-- Excellent surface-to-air-defences of their own, which are in turn capable of deflecting most any attempted air raids or missile strikes aimed at the Neo-Khanate itself.
-- Ludicrously good logistics.
-- A highly militarised society, completely unhindered by even the slightest hints of democracy.
-- Within the Neo-Khanate, many cultures exist, and the governing policy is "get along, or else". A religion that tries to impoe itself on others is a religion whose adherents get turned into dog food by the close of the year.
-- A policy of granting immediate citizenhip to any nation or regions that joins them. As a mater of routine, the existing bureacracy is purged (sometimes up to 100%), and a new, stream-lined governmental apparatus put in place. Taxes are lowered by 50% at minumimum, often they are lowered by up to 80%.
-- Conversely, a policy of ruthless conquest, where resisting region or cities are literally exterminated. In case of 'betrayal' (i.e. a region submits, but then rebel activity begins) the entire region is depopulated, in some very attention-grabbing form (like mass crucifixions, pyramids of skulls, organised gang rape of literally every woman who lives there...)
-- Ground forces are presumably very numerous, but because the focus is on the "aerial blitzkrieg" strategy, they're presumably not the best the Neo-Khanate has. Ruthless butchers who slaughter anyone who resists in already-conquered regions where trouble arises. (As a key point: regions that join voluntarily are treated very well, and don't typically need occupation, nor is stationing many troops there desired.)
-- Probably a shit navy, if any to speak of. This means that while missiles and advanced strategic bombers may inflict horrors across oceans, mass projection of fighters across vast oceanic distances is a no-go. This mimics the weakness of the OTL (land-bound) Khanate to some extent, at least.