Pegg brings up all these points in his essay, but he also raises one that I hadn't really thought of before: the zombie as metaphor for death.
Where their pointy-toothed cousins are all about sex and bestial savagery, the zombie trumps all by personifying our deepest fear: death. Zombies are our destiny writ large. Slow and steady in their approach, weak, clumsy, often absurd, the zombie relentlessly closes in, unstoppable, intractable.
However (and herein lies the sublime artfulness of the slow zombie), their ineptitude actually makes them avoidable, at least for a while. If you're careful, if you keep your wits about you, you can stave them off, even outstrip them - much as we strive to outstrip death. Drink less, cut out red meat, exercise, practice safe sex; these are our shotguns, our cricket bats, our farmhouses, our shopping malls. However, none of these things fully insulates us from the creeping dread that something so witless, so elemental may yet catch us unawares - the drunk driver, the cancer sleeping in the double helix, the legless ghoul dragging itself through the darkness towards our ankles.
Exactly right! And that only begins to scratch the surface of why the metaphor is perfect. This is also why the zombies must always win in the end. You can cheat death--for a while--but the horde of walking dead have time on their side. And those trying to cheat death damn well know it!
Enjoy Zombie Day by watching some good zombie movies. You owe it to yourself.