This matter of dominion includes a sphere or a realm. There are three points related to this sphere:
Man must have dominion over the seas. The seas are the lodging place of the demons (Matt. 8:32; 12:43). Thus, the sphere of God's dominion must include the seas.
Man must have dominion over all things in the air, which is the place where Satan and his angels are (Eph. 2:2; 6:12). There are evil powers in the air with Satan as their head. Ephesians 2:2 describes Satan as the prince of the power of the air.
Man must have dominion over all things on the earth, the field of Satan's activities. Satan is very active on the earth (Luke 4:5-6). So, here in Genesis 1:26 it especially says that man may have the dominion "over all the earth." The earth has been usurped by Satan. Thus, it needs to be ruled over by man, God's representative.
Remember that the sphere of God's dominion which He committed to man includes three sections: the seas, the dwelling place of the demons; the air, the place where Satan and his angels are; the earth, the field of Satan's activities.
When the Lord Jesus was on this earth, He had to deal with Satan, fallen angels, or demons wherever He went. That was why the Lord Jesus rebuked the wind and the waves during a storm. The wind came from the fallen angels in the air and the waves came from the demons in the water. The Lord told the wind, "Stop" and the waves, "Be calm." Immediately the wind ceased and the waves were calm. The fallen angels and the demons were subdued and overruled by the Lord Jesus. If we know how to read the Bible, we will see in the four Gospels that the Lord Jesus exercised God's authority over the seas, the air, and the earth. This is the sphere of God's dominion which He committed to man.