The "End of History" here means that there are no more any serious ideological competitors against liberal democracy. Religious fundamentalism, Chinese and Russian systems and their reactions so far prove it. China and Russian are reacting and defending against liberalism, they are not providing anything new, they are not doing anything better. No solutions, only reactionary rejection and nihilistic decay.
As long as no nother political structure can provide citizens with the levels of wealth and personal liberties that a liberal democracy can, this is the end of history.