Yes. The story is very well done. Your character has a great arc and is barely even a "hero" in the beginning.
He is dropped in the quarantine zone as an agent for the government and only pretends to be aligned with the good guys to figure out who and where a rogue agent went with the cure.
When he finds the rogue agent, to get in good with him, your character starts doing errands for him. Extortion and passing on threats.
There are things to do, mostly centered around killing zombies, yes, but as the character unlocks more abilities it is a lot of fun.
There is a trap that is a car rigged for an electrical explosion. When you activate it, the car alarm goes off and the zombies are attracted to sound. They go to it and BLIZAPP!! electric blast sending them cripsy and flying.
The car stays intact, so you can run up to the car and reconnect the battery and do it again.
There are time trails you can do, racing over rooftops, challenges of how many zombies you can kill a specific way in a set time.
There are civilians you can save from militia or zombie attacks.
The government drops supplies in the zone and when they come, you can get to it before the militia does.
There's side mission and some "farming" of items to craft other items.
There are zombie nests that are advised that you go at night. During the day, the scariest zombies are in the nest, at night they go out so the nest is safer to destroy.
Highly recommended game for a zombie fan.
Part 2, supposedly, isn't as good. They added a weird game mechanic where you gotta keep injecting a cure and the use of sound design and ambience are not the same.