"Bobby is little overweight, a little unfit, and in a lot of trouble."
The player guides an average over-weight guy to safety, while surrounded by everyday hazards (zombies, aliens, etc.). The twist is that the closer that every hazard gets, the higher his blood pressure gets, which can also affect his health. The player needs to keep eating to top up his health, but this can also speed up his blood pressure increase, affecting his health faster. If his blood pressure gets too high, he'll suffer a heart attack.
The player has to survive long enough to reach safety.