Real cool idea honestly. Music and art were cool.
Notes:
I didn't even know your goal was to kill the zombie. I ended up racking a high score due to me just running and getting so far away. It is a lot more beneficial in the long right.
As soon as you kill a zombie a whole horde appears and they are fast, making it more difficult for you to run away. It would have been since if the shoot mechanic was more rewarding like 2x and 3x have longer ranges and more damage. It would have also been nice to add a kite mechanic so that if you choose to shoot it pushes you back when you fire to give you more time to avoid the zombies.
Overall nice work on entry!