The major issue here is how you define victory in the modern sense. There's no doubt that Genghis was incredibly successful, but many question whether simply occupying all other civilisation's capital cities amounts to his claim of world domination. This view is supported by population statistics which show that at its height in 1832 the Mongol empire only controlled 24% of the world's population. The same figures are also used to dispute the Aztec claim on the grounds that whilst they may have been culturally important, this only applied to the 21% of the world's population living within Aztec borders.

The Russian claim appears more clear cut after the launch of the Alpha Centuri mission in 1982, but I would posit that we should wait until the mission is successful before we credit Catherine the Great with a victory. Unfortunately taking the 20 year rule into account we won't be able to discuss that until 2036.