Not everyone who believes in some sort of higher power believes in the type of God who imprints the moral law on our hearts. Deism tells us that God created the world and then left us on our own - that He has no interest or involvement in our lives. If the moral argument holds, God can’t be like this, because He obviously cares how we respond to each given specific situation in our lives. God must want to be involved with us.
Additionally, God can’t be the “god” of pantheism, who is inseparable from the earth itself. Nature can’t be synonymous with God since, as we’ve seen, nature can’t account for our moral obligations. Further, moral law transcends the material world, and the God who gave it is transcendent also. Though God “stoops down” to be involved in our lives, He is far above and much different than us.