I don't think it's accurate to say that "liberal western-style democracies" are the natural end-state. I think it's accurate that history has shown that such democracies work
better than authoritarian regimes for various reasons -- largely economic.
I don't think that China's recent success disproves this. China spent decades experimenting with ruthless authoritarianism, and wound up decades behind the world. They relaxed their hold for a time, and experienced massive catch-up growth -- growth they would have experienced much earlier if their government had been properly managed.
The real question is whether they'll be able to continue that growth if they turn to a much more authoritarian model, which seems to be the direction they're going. And I'll be frank that there seems to be very little historical evidence that this approach will lead to continued economic (and thus political) dominance. In fact, all signs point the other way. It's just unfortunate that we keep trying the experiment.