From what I remember of the in-series explanation of this particular virus, it only re-animates the baser parts of the brain--what is sometimes referred to as the "lizard brain"-- that control the functions of breathing, heart function, coarse movement, and the base/primal instinct of hunger. I don't think that the walkers need to feed on flesh as a means of survival, more that this virus uses that instinct to propagate itself.
An easier way for me to see it is:
Imagine your body is similar to a computer. What the virus does is power down the entire system and reboot into safe mode, to an extent. And after booting back up, the virus makes connections to other computers and spreads...lather, rinse, repeat...until it has infected "all" of the computers in the world.
Does anyone have anything to add to that or want to refine it?