What does it mean that mankind was made in the Image of God? At its most basic, "image" as used in Genesis 1 refers to a rendering, something cut out like a sculpture or carving. Verse 26 uses "likeness" to describe the nature of that "image", which captures quite well the thought of resemblance. Therefore, the image of God in mankind is a representation in the created world that resembles God--an optical counterpart, if you will, which is not of the same stuff as the original but looks the same nonetheless.
However, God is not corporeal so the likeness in question cannot refer to the physical or tangible realm--it must refer to something metaphysical, something spiritual. Our physical being certainly says something about the attributes of its Creator, but our physical being is not what reflects the image of God. So what do we know about God that isn't physical or visible? He is spirit. He does as he pleases. He is creative. He is love. He reasons. He communicates. He has a will. And in the fullness of all that he is, he rules.
Now, it would be a mistake, in concentrating on that last characteristic, to assign the image of God primarily to the mere exercise of sovereignty or dominion. God's nature is not circumscribed by the attribute of sovereignty, and so being in the image of God cannot be solely about dominion. Besides, ruling, as commissioned in mankind, was concomitant upon them being made in God's image rather than being a reiteration of what it meant that they were made that way (i.e v. 26 is an expression of synthetic rather than synonymous parallelism).
But even if one were to insist on making this error, dominion, or ruling, is still founded upon the ability to do what one wants with what is dominated. The more limited a being's degree of freedom to act is, the less that being can be said to be exercising dominion. You see, sovereignty is really, at its most fundamental, about doing as one pleases with what one is sovereign over. Therefore, it is really no stretch at all to see that doing as one pleases, whether it is this or that (i.e. freewill), is essential to the nature of God, to the concept of sovereignty, and by implication, to the image of God in man.
In fact, a being cannot be said to be in the image of God without having freewill.