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A mediator is only necessary when there is an agreement for two or more parties to agree to or discuss. God's promise to Abraham, and the inheritance that will come from that in the future, was not something that had to be negotiated. A mediator was not necessary, because there was only one party—God—who was agreeing to do a certain action. God's promise was His intent to carry something out, and so it was not necessary for there to be a mediator.
The Mosaic covenant required a mediator. Moses stood between the Rock and the children of Israel. The Israelites did not want to deal directly with God (Exodus 20:18-21) and instead requested that Moses speak with God and then speak to the children of Israel. The Old Covenant was set up with a high priest as an intercessor, who would stand between God and the people. The system, the covenant, did not allow for a personal relationship to develop between God and an individual, except in the rare exceptions where God made it happen. But it was not available to the average Israelite.
God's promise is sure! Abraham and the others in the "cloud of witnesses" all died without receiving the promises in their entirety. But the spiritual children of Abraham still stand to inherit eternal life, the earth, etc. This was not an agreement or covenant, but a promise.
When the covenant was ratified at Sinai, Moses was the mediator for only physical Israel. The Gentiles, the rest of the people who would be the spiritual descendents of Abraham, were not represented. Because of this, the agreement made at Sinai could not affect the unrepresented people. This is why the Old Covenant, or the Mosaic Covenant, is not binding anymore: Christ, the Seed, came to earth as a man, and the temporary covenant between God and Israel became obsolete.
God's law did not become obsolete, though—God does not change, and so His definition of what is right and what is wrong does not change. If it was wrong for the Israelites to commit adultery or fornication, it is still wrong now. If it was wrong for the children of Israel to break the Sabbath, it is still wrong now. Obedience to God's law was a condition of the covenanted agreement, but doing away with the covenant does not do away with God's law!
David C. Grabbe