Gaining control of "quarter of the world", as the episode stated, could be accomplished simply by becoming President of India. That's also a pretty good approximation of "from Asia through the Middle East", as the extent of Khan's realm was described, assuming that taking control of India would also entail conquering Pakistan (a surefire way to get a good and popular hold of India!).
The episode further states that the supermen came to power by simultaneously taking control of over forty nations. This takeover was also described by our heroes as a collection of "petty dictatorships". Sounds like a series of palace coups instead of ruthless military conquest and massacre of the masses. It wouldn't be that difficult to imagine that some 40 nations in southern Asia and the Middle East would be in a situation where a palace coup would be possible - and if a determined group engineered all those coups simultaneously and under a joint goal, the individual nations would not take advantage of instability in their neighboring countries as would otherwise be the case.
I reckon it stretches credibility a bit too far to have the current situation with the War on Terror, Iraq invasion, etc, happen after Khan
But there is no indication that the Trek universe would "have" the current situation. No mention has been made of an Iraq invasion by the United States, for example (although Iraq has always been a target of US ambitions, and probably will remain so quite regardless of local and global events, because Iraq has oil). Nothing has hinted on a War of Terror, either - quite to the contrary, Data in "The High Ground" praised terrorism as an (apparently relatively benign) means by which Ireland gained its independence in the early 21st century, an argument he would not have made had the current feelings about global terrorism existed and left their mark in the history books.
At most, there has been a brief visual of an aircraft impact on the WTC tower in one ENT episode - but no exposition to connect this visual with terrorism. For all we know, this was a harrowing aviation accident in the Trek universe. Or possibly a Soviet strike, an Econ attack, part of General Green's dastardly devices...
Timo Saloniemi