The short answer is no, you don't have to run with Zombies, Run! at all.
The long answer; we've designed the app so that people of any running (or walking) ability can use it, and you won't be penalised for not being able to go at a certain pace. The main goal of our app is to get you to want to go and exercise, even if it's maybe a bit rainy out or you don't really feel like it! You can move at your own pace and discover the story as you go.