I'll just say this as my final point. The reason I'm somewhat vocal on this is because I think there's no reason to categorize something as different if it really isn't different. Categories exist for the very reason to create categories for similar things, not exactly the same things, but general things.
Last of Us most certainly is deeply inspired by zombie movies and has several direct references to zombie media, and the infected definitely behave similar to depictions of zombies. The story also hits a lot of the same notes as a zombie story. Downfall of our known civilization by cause of some form of infection. Focus on characters, drama, social messages, and symbolism using zombies as a backdrop and a catalyst for other elements.
Basically, if they look like zombies, act like zombies, sound like zombies, have everything in common with zombies, even not being called zombies they have in common with zombies, and in a story that is the same sort of thing you'll see in zombie movies, then yes, they are zombies.
The Last of Us and Resident Evil Zombies are also listed on the Zombie wikipedia as type of zombie:
http://zombie.wikia.com/wiki/Types_of_Zombies
It's not really important, zombies are zombies. That's a-okay. What I don't like is people trying to say they aren't zombies because of some perceived notion that makes what Last of Us does less interesting or meritable, because zombies are overused or some trife like that. It's like some people are afraid to call it like it is because of some pre-conceived notion of the word zombies because of over-representation which might delude something they hold special and want to stand above the norm. But that's achieved by personal merits, and pulling off what it does well. And it pulls off zombies well. But they're zombies.