The initial state selected time-dependent wave packet method has been extended to calculate the total reaction probability for atom-triatom reactions with total angular momentum J>0 by treating both bonds in the triatom reagent reactively. The total exchange and abstraction reaction probabilities for the title reaction with J=15 calculated with 2 K-blocks (the projection of the total angular momentum on the body-fixed axis) show that one has to treat both OH bonds in the H2O reagent reactively for the exchange reaction, but for the abstraction reaction one can treat one OH bond as a spectator bond to get accurate results. This is in accord with what had been found for the total reaction probabilities for J=0 [Phys. Rev. Lett. 89, 103201 (2002)]. The J=15 reaction probabilities also show that the CS (centrifugal sudden) approximation is inadequate for the title reaction, in particular for the abstraction reaction. The integral cross sections for the abstraction reaction, calculated without the CS approximation but by freezing one OH bond in the H2O reagent for the ground and first vibrationally excited states, are found to be substantially larger than the corresponding CS integral cross sections. However, the integral cross section for the ground vibrational state is still much smaller than the existing experimental result. Since the treatment of freezing OH bond is not expected to introduce any noticeable error, it is conceivable that the experiments overestimated the integral cross section for the abstraction reaction.