No, not anymore. Dominion means to have authority over. For instance, God has authority over all creation, Jesus has authority over the church, and parents have authority over their young children. In the beginning, God said it was good for man and woman to have authority over all the earth (Genesis 1:27-31). The instructions for how to exercise that authority were to “tend and keep the garden” (Genesis 2:15) while eating only fruit and vegetation (Genesis 1:29), except for that which grows from the tree of knowledge of good and evil (Genesis 2:17).
Instead of exercising our divinely appointed authority by following God’s instructions to maintain and take care of the garden, we tried to establish our own authority by eating from the one tree we were told not to eat from. This led to a cascade of events the caused the world to fall into ruin, eventually resulting in God flooding the whole earth and restarting with Noah and those aboard the ark.
When Noah got off the ark and started killing animals, God responded by saying “the imagination of the human heart is evil from youth” (Genesis 8:21). Nevertheless he blessed us and told us to multiply, along with all the animals, exactly as he did after first creating us in the beginning, except with one marked difference. Instead of granting us dominion over all the animals and over the whole earth, he tells us animals will be afraid of us and that we will see them as food (Genesis 9:1-2).
So by going against God’s instructions and instead attempting to establish our own authority, we lost our divinely appointed dominion that was given to us in the beginning. God calls us to repent and to turn back to him, to “remember from where we have fallen and to do the first works” (Revelation 2:5). Only by turning back to God and living according to his ways can we regain our divinely appointed authority over it. God is ready to forgive and to give us to eat from the tree of life. All that is required is to submit to his authority instead of stubbornly insisting on doing things our own way.