What drains your battery (besides the obvious screen, and data connection), is your CPU running.
Most battery savers and task killers just remove the background tasks or services. When an app wakes up your CPU on its own when your device is in deep sleep, that will drain more battery.
ShutApp saves battery in a different way. It actually stops apps from running in the background, stopping them from using RAM, CPU and wakelocks. That's why it can significantly improve battery life.
I'm sorry but this is a basic functionality of task manager in every android device. I don't see the point in using this. Besides ShutApp is another application running on your device that eating up HW resources. So using ShutApp kind of defeats the purpose it was made for.