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From what you have quoted I would say that we can kill animals for food.
"Just satisfaction" meaning to satisfy our reasonable needs - e.g., we need food to live.
That we need to treat them kindly speaks to how they are allowed to live and that we "dispatch" them with out causing pain or distress.
This, in my opinion, affects the eggs and chickens we buy - an industrial form of agriculture that has seen much ill-treatment of the animal in the name of profit.