Well, first off I would highly highly scrutinize this blog's claim and would not under circumstances accept anything written in it as authentic until you see something from the "source". None of the claims made in the blog can be substantiated and in many cases I think he's reading into it a bit too much into a document IF the document is reliable or not. But that is neither here or there.
If I could venture my own two cents. just the very mention of the word Zombie or Zombie apocalypse throws out any sense or form of realism period as the very idea is beyond logic or reason to begin with. Another problem is with the definition of a Zombie as they are supposed to be a creature without a soul in addition to not possessing reason or logic nor free-will and are therefore instinctive creatures, thus the Catholic church would place such creatures into the realm of beasts and not human beings. they are life, but they are not human beings anymore. the very idea of resurrection is that body and soul are resurrected (or in the very least the soul is resurrected and glorified) so it can be ruled out immediately that Zombies are not a part of the resurrection but an abomination to that idea. Also given that ethically if a Zombie is about to kill you and you kill it in self defense, the act can be compared to a Lion about to gore you. You are acting in self preservation and in doing so have not killed another human being in the process. Therefore the act itself is not a mortal sin. It don't think it's even venial since the odds are you acted instinctively, acted without the use of reason (or at least reasoning in that, "act now or die"). Any act of cruelity is considered a mortal sin regardless, aka.. torturing an animal or the like.
Conclusion: treat Zombie's like an irrational creature and look up what the Church says about that.
Hope this helps.