There is a little aside here that we should get to before we go past it, but it will not take long. When these verses are combined with Genesis 1:28-29 and Genesis 4:1-5, it shows that this is not mankind's introduction into eating animal flesh. You can read verse 3 in chapter 9. But in Genesis 1, what God is doing is showing that all life, animal and human, ultimately depends on vegetation: I have given you all the green herbs to eat. And that is true.
Remember Genesis 4:1-5. Abel brought to God an animal sacrifice. That shows us that God had already showed them that their dominion over animals extended to the place that they were able to take an animal's life. God was well pleased with Abel's animal sacrifice. He was so well pleased that it is recorded back in Hebrews 11 that it still witnesses. So God was not overly concerned about the killing of an animal, but what we need to understand is that they understood about sacrificing, and some of the sacrifices had to be eaten. That was a requirement of God. The sin offering was to be eaten, part of it anyway, and the peace offering was to be eaten.
I think that these verses clearly establish that animals' well-being is directly tied to man's exercise of his free moral agency. If a man chooses to obey, God will bless both animals and man. As the animals are blessed, so is man; as man is blessed, so are the animals. If a man's livestock is not eating, then it is pretty certain that the wild things are not eating either.
It is interesting to note the sequence here, especially in verse 15. Much of man's sense of physical well-being is usually illustrated in the Bible by a full stomach. It is an illustration that God uses that if your stomach is full, you feel that things are all right in the world. What He is saying is this: if you look at the sequence, that the animals must first be blessed before the blessing accrues to man.