Some of these points make sense, though others are decidedly defeatist and manic-depressive. But the one that grabbed my attention the most was no.3, because it's one I myself have ruminated on. In a nutshell, I think Yahtzee's got the right idea, but not for the right reasons.
Or let me put it another way, not for the same reasons I think zombies represent life after death. The way I see it, zombies don't represent life after death just because in some forms of media they're depicted as continuing to perform certain ingrained habits they picked up in life and continue to follow by reflex.
Zombies represent life after death because if there is no such thing as a soul or an afterlife, then all we are as beings are organic machines. If being animated through one means or another is all it takes to be designated as "alive" then there would really be no difference between us and zombies than the kinds of actions we perform. Pre-zombie people would talk, walk, sleep, eat, screw, etc. while zombies would walk (well stagger, unless they're the Dawn of The Dead remake types), eat and maybe run for elected government offices.
But when we look at zombies, we see a severe, unavoidable difference between ourselves and them. We feel, we express emotions, we do things beyond simply what's necessary to remain functional. The shambling corpse gnawing on the postman's severed arm doesn't. In spite of the fact that both a living person and a zombie are both functioning and animated in some way, there's a noticeable, obvious absence of SOMETHING in the zombie. Something that makes it less of a person than a living human being, even less than an animal. What's missing? Is it maybe the soul? And if so, where did it go?
These are the sorts of things that zombies hint at through their very existence in media and fiction; the idea that there's more to a person than just their bodily functions.