In Covenant Theology, the Covenant of Grace is a singular overarching covenant God makes with his people. The various Biblical covenants are understood to be expressions or administrations of this singular Covenant of Grace.
Here's what the Westminster Confession says about the Covenant of Grace:
Man, by his fall, having made himself incapable of life by that covenant, the Lord was pleased to make a second, commonly called the covenant of grace; wherein He freely offers unto sinners life and salvation by Jesus Christ; requiring of them faith in Him, that they may be saved, and promising to give unto all those that are ordained unto eternal life His Holy Spirit, to make them willing, and able to believe.
This covenant of grace is frequently set forth in scripture by the name of a testament, in reference to the death of Jesus Christ the Testator, and to the everlasting inheritance, with all things belonging to it, therein bequeathed.
This covenant was differently administered in the time of the law, and in the time of the Gospel: under the law it was administered by promises, prophecies, sacrifices, circumcision, the paschal lamb, and other types and ordinances delivered to the people of the Jews, all foresignifying Christ to come; which were, for that time, sufficient and efficacious, through the operation of the Spirit, to instruct and build up the elect in faith in the promised Messiah, by whom they had full remission of sins, and eternal salvation; and is called the Old Testament. (WCF 7.3–5)
Here's what Horton says:
Like the covenant of creation, this covenant is made between God and human partners—in this case, fallen Adam, Seth, Abraham, and David. It is in this covenant that provisions are made for offenders, based on another's fulfillment of the legal covenant on their behalf. (Introducing Covenant Theology, p105)
So the Covenant of Grace is between God and all of his people, anyone who will receive in repentance the offer of free grace and turn to God in faith.
But the parties of the Noahic covenant appear to be different, not just humans, but all life of the earth:
Then God said to Noah and to his sons with him, “Behold, I establish my covenant with you and your offspring after you, and with every living creature that is with you, the birds, the livestock, and every beast of the earth with you, as many as came out of the ark; it is for every beast of the earth. I establish my covenant with you, that never again shall all flesh be cut off by the waters of the flood, and never again shall there be a flood to destroy the earth.” And God said, “This is the sign of the covenant that I make between me and you and every living creature that is with you, for all future generations: I have set my bow in the cloud, and it shall be a sign of the covenant between me and the earth. When I bring clouds over the earth and the bow is seen in the clouds, I will remember my covenant that is between me and you and every living creature of all flesh. And the waters shall never again become a flood to destroy all flesh. When the bow is in the clouds, I will see it and remember the everlasting covenant between God and every living creature of all flesh that is on the earth.” God said to Noah, “This is the sign of the covenant that I have established between me and all flesh that is on the earth.” (Gen 9:8–17, ESV)
My reading of this passage is that the Noahic covenant is a unique one, when God bound himself to a covenant not just with people, but with his animal creations as well. Let no one say God does not love his animals!
How do Covenant Theologians explain the Noahic covenant? If all the Biblical covenants are administrations of the Covenant of Grace, how do they account for the different covenant parties? Surely they would not say that the non-human animals are part of the CoG; Jesus did not die for the sins of animals. Do Covenant Theologians say that the Noahic covenant is really only with humans, that the parties are God and humanity with animals being non-party beneficiaries, despite God five times saying that it was with "every living creature" or "all flesh"?