How does this circuit start up?

Normally we are using the start-up resistor. But in this case, there is an internal MOSFET between SW and VCC pin. And this MOSFET will provide a start-up current.

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At the top of the block diagram on page 2, there's a MOSFET that functions as a current source connected between SW and VCC that can withstand the full line voltage. It passes a tiny current (via winding "A" of the transformer) that doesn't cause too much dissipation inside the device. This current is not sufficient for operation of the switching regulator, however.

This current source charges the capacitor attached to VCC until it reaches Vccon, at which point, the switching begins (powered temporarily by the charge on the capacitor) and larger amounts of power can be transferred via the auxiliary winding "B" on the transformer to keep things going continuously.