I have too may problems with the zombies. The Shovel does too little damage to start, and you have to keep retreating to avoid being hit. It doesn't help that the zombies have no walking SFX so they can easily sneak up on you while your digging.
I also felt it strange that the zombies seemingly spawn from a random direction instead of say, the graves you have already dug up.
It's a good concept, but I'm finding it a too frustrating to play.