The Gate feeds off them not in a traditional sense, but psychologically (this is a 5th dimensional being, its needs cannot be fully understood) The Gate destroys the emotions and free will of dolls and contractors, enjoying a heightened time of feeding when a contractor reumanates.
The Gate creates dolls and contractors to 1. This means the Gate has the human race trapped on Earth, unable to escape its grasp. It is mentioned that attempts to send rockets into space resulted in them vanishing. 'Feed the gate'? Yup, if its alive, that means it must sustain itself somehow. It probably has to do with the individuals potential to feed the gate and to not 'burn out' like Havoc did. Why it chooses certain people to be dolls or contractors is unknown. It is what creates the contractors and the dolls. This is evidenced by the fact that the gate seems to be aware of what happens to it and it is able to react to stimuli (like when the 1st team to enter the gate was mostly killed off) The gate is also active in other ways. They are not a place, but rather a living being (perhaps 5th dimensional?). What are the Gates? The gates are one in the same thing.
Darker than Black is an anime series that often leaves people with a lot of questions
