The double rating with VA and Watts is that way, that both numbers can be limiting. For the 1500 VA, 900 W example they claim to deliver up to 1500 VA if the real power is below 900 W. So for a load with PF of 1 they can deliver up to 900 W. They can still deliver up to 900 W even if the power factor gets less good, down to about 0.6. With a power factor that is even worse (e.g. 0.5) the VA rating would be limiting - so no more than 750 W at a PF of 0.5 as this would reach the 1500 VA rating.
The power factor is used to describe two possible effects of the load. One are phase shifts (e.g. from an inductive load like an AC induction motor. The other are nonlinear loads like many LED lamps or old / poor DC power supplies - these cause a non sinusoidal current flow. For something like an transformer the PF is the correct number to describe the losses. However it is not clear that the electronics in the UPS also reacts similar to both types of PF, so the VA rating might not be valid for all cases. At least there is an additional limit on the peak current, even if the VA rating is not exceeded. So it is a good idea not rely on the full VA rating of the UPS.