I believe the Mughal rulers of India claimed direct descent from Genghis Khan, but I don't know if there are any men alive now who can claim direct male descent from the Mughals.
There almost certainly are, though they may well not know it, since the Mughals of the Timurid Dynasty of Samarkand [until lost to the Uzbeks in 1496] who traced their descent from Tamerlane ruled until the British crown assumed sovereignity over India on 01 November 1858 could follow their own royal heritage from Tamerlane himself to the last of the *Emporer Kings of Delhi*, Bahadur Shah II, deposed on 29 March 1858, and exiled to Burma, where he died with the age of 87 years. Though he was the last of his line, several Emporers and Princes fathered 50 known sons or more, so while a rightfuil heir would be difficult to determine, membership in the bloodline would not be.
Since status then was determined by the size of an individuals mensab of loyal troops, with a unit of 10,000 horsemen and footsoldiers reserved for the Imperial Princes, units of 7000 for a noble or vassel prince, and those with 500 or more being known as Amirs being commanded by those holding a bewildering array of titles and rankings, perhaps the answer would be to see which potential leader could best and most rapidly recruit, equip and field the most efficient and effective military organization.
After all, that sort of conflict is an old sport in that region, and it appears that the season for such activities is again nearing. And that's the real Sport of Kings.
-archy-/-
Bandhar Shah Zafar.............................Tamerlane:
-archy-/-