Good point. Strictly speaking, the Khilafa or Caliphate lasted a few decades after Muhammad's death before it was superseded by the Umayyad Dynasty based in Damascus, which was displaced after about a century by the Abbasids based in Baghdad. That last dynasty was destroyed in the thirteenth century by the Mongols, and there has never been a unified "world Islamic state" since---not even the Ottoman Empire had all of the Islamic ulema under its sovereignty, but had Islamic rivals in Morocco, Iran, Central Asia, and Mughal India.
If these jerks want to blame anybody for the breakup of the Khilafa, they should blame Genghis Khan and the Mongol Hordes.