God gave animals the green plants or herb, he gave humans every seed-bearing plant on the face of the whole earth and every tree that has fruit with seed in it. So likely, it was God giving over "everything that moves" to the animals. Regardless, God is responding to sin and humans hardness of heart, he had just destroyed the earth due to all this sin and was starting over! In the beginning before sin entered the world he prescribed vegetation to all of us, humans and non humans, this was to be their food, this is his perfect will for us!! What does it mean to have dominion? Does it mean domination? What does it mean to be made in the image of God? Does it mean we look like him or have some attributes of God? Or does it mean we are supposed to embody God over that which he puts us in charge of? In the beginning this is what he did, he put us in charge over the rest of the creation that he made. This is a huge responsibility and role, to carry out God's good instructions, to see that the whole creation under us flourishes!This pretty much set the stage for things until Christ returns.
Genesis 9
1 And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth.
2 And the fear of you and the dread of you shall be upon every beast of the earth, and upon every fowl of the air, upon all that moveth upon the earth, and upon all the fishes of the sea; into your hand are they delivered.
3 Every moving thing that liveth shall be meat for you; even as the green herb have I given you all things.
4 But flesh with the life thereof, which is the blood thereof, shall ye not eat.
5 And surely your blood of your lives will I require; at the hand of every beast will I require it, and at the hand of man; at the hand of every man's brother will I require the life of man.
The following is from an article that I encourage you to read. Humans are full of cognitive dissonance or double mindedness. This article paints that picture quite clearly: A Beloved Swan Named Faye in a NY Pond, Killed and Eaten
"At the beginning of Creation ... before sin entered the world, God established what our relationship toward animals should be. Animals share the sixth day of creation with humans (Gen 1:24–31). In Genesis 2:18–19, Genesis 1:29, animals are not created as resources or food for Adam, but rather companions with Adam. There was no predation or killing of one another. So from the beginning, God’s intention for animals and humans was to coexist in harmony as companions with one another with the earth as their shared home. In Genesis 2:15, God placed man in the garden to have dominion over it, to care for or cultivate it and maintain or keep it. The words care/cultivate in the original language is עבד, transliteration `abad. It means to labour, work, do work; to work for another, serve another by labour. The words keep/maintain in the original language is שׁמר; transliteration shamar. It means to keep, have charge of; to keep guard, keep watch and ward, protect, save life. We get an unmistakable image of the dominion given to us as a responsibility to “serve” and “protect” the garden’s inhabitants and the garden itself. Being made in God’s Image is the embodiment of God in order to care for and watch over that which God created."