The new CR 614.16 is about replacement effects for effects that create tokens or put counters on a permanent. The new part is that “they also apply if another replacement or prevention effect does so, even if the original event being modified wasn't itself an effect”.

Does this change the answer to “Anointed Procession and Kalitas”? I guess now it doesn't matter whether my opponent's creature dies due to a Fatal Push or because of lethal damage by Shock or combat, because the replacement effect of Kalitas, Traitor of Ghet applies in both cases and that's enough for Anointed Procession to be applicable too. Right?

Regards,

Mario Hassler

Indeed, this ruling has changed. Kalitas + Procession now always makes two zombies rather than one regardless of the reason why the opponent's creature is dying, for exactly the reason you stated.