I voted yes and no. I don't think zombies are any less relevant a game genre, it's the experiences had with them that are getting old and the characters that are surviving that mean less and less to the audiences. Don't explore zombie stories unless you've got a great monster story that is worth telling. The common thread for every monster story is the relevance to current events the common views of the audience and of course fears of the masses. It's been polled that the greatest fear most north Americans have is the corruption of authoritarian organizations like governments. Zombies are the most meaningful monster in this day in age because they represents our lack of trust in the communities that surround us. They are the mindless masses that devour free will and steal the soul from an individual and turn them into, just another zombie. We're afraid of that because life often feels that way.
As for the gameplay you mentioned, it all came off a bit general. Nothing really caught my eye. You mentioned it's 3rd person. How come? Is the control setup unique in some way or are you planning on bringing something new to the character design that makes the 3rd person view meaningful. When resident evil did it they used complex controls and slower character animation to build suspense. You could use this and explore a character evolving from bumbling, terrified zombie chow into a militia Zed-killing expert with a scaling skill system in the background. Many characters are quite flat in most zombie games, where the writing changes (maybe) but the player's skill defines the character's skill making replay lack suspense. If the character's animation actually helped describe the character and evolved as the player survived encounters and the characters actually bore the experience of surviving this horror it could be refreshing. To make this less linear you could have encounters that you fail but don't die, where another character saves you and you don't earn any experience from the encounter but grow a connection with the character that saved you, etc.
As for story bits, something you could try is moments where the player is about to die, you could flash back to moments that show the character learning skills from a mentor like martial arts as a kid or firing a handgun with an uncle, etc. These playable moments would test the players skills in the moment and if they succeed they're returned to the main timeline with all the zombies in that area cleared. (hope that made sense) Failure is obviously up to you how you handle it.
My last suggestion, don't focus so heavily on the weaponry. There is a lot of this out there and it takes players out of the "monster moment" that I feel you be focused on trying to create. I would have a "go to" weapon your character prefers, a few throw away alternatives and some fun mods the character can get creative with in the mid and late game but I wouldn't over do it.
Remember to prototype it to undeath