If you want to do zombies and corporate evil, it is much more scary if you start with the corporation already in power, like they are now. Maybe it could take place sometime in the future, where corporations have amassed such power with their products that they have slowly infused the "common" population with additives or nanobots or something that have effectively turned those people into zombies. Maybe they have even caused physical changes, like making the people stronger and more resilient and resistant to pain so they can be better workers, and so they are inexpensive to maintain. They would be like worker bots but better. Worker bots require maintenance and a lot of expensive raw materials. But biological organisms maintain themselves. They reproduce very cheaply, and as long as you feed them some kind of nutrient slurry they keep on working for decades, and sometimes even a century. All you have to do is highjack their minds.
The game would probably involve the player as some sort of outsider, either a rebel or a freed zombie, who goes against this entire world. And once the people in charge see there is an intruder, they would broadcast some signal that would make all their zombies hostile towards you.
If you're willing to play with the traditional idea of 'zombie' and move away from the dirty and decaying corpse idea, you could come up with some pretty terrifying scenarios--imagine a "Prozac Zombie," a creature that has been chemically lobotomized and is now incapable of feeling anything other than a sick and unnatural happiness no matter what happens. You shoot it and it keeps smiling at you. You blow its arm off and it laughs like someone who just heard a funny joke. Imagine being beset upon by a hoard of people smiling like it's their wedding day and saying pleasant, neighborly things as they walk towards you and try to rip you apart. They are chemically unable to feel pain, fear, or anything unpleasant, and no matter how you kill them they die laughing and smiling. They would look like normal people except just a little bit off, and the world would be very neat and orderly, maybe no different than how it is today. It would be kind of the inverse of a Zombie Apocalypse--rather than destroying society, the zombies ARE society.