So, within the covenant, Abraham is a third party beneficiary. Abe is not held to account to keep any side of the agreement. But he benefits from the results of the covenant.
That's the whole nature of early biblical primogeniture in which the firstborn inherited everything the father had. In Abraham's case that included God's promises to him. Any other sons received their allotments of the inheritance from the firstborn, not the father. So likewise we receive our allotment of the inheritance from Christ, the firstborn, just as Abraham saw receiving his inheritance of the land from his seed (Christ) in the resurrection because the promise was to him, the firstborn (Genesis 15:18).
This is why Israel received their allotment of the land from Joshua of the tribe of Ephraim, who was the firstborn.
They shall come with weeping, and with supplications will I lead them: I will cause them to walk by the rivers of waters in a straight way, wherein they shall not stumble: for I am a father to Israel, and Ephraim is my firstborn. Jeremiah 31:9
Israel had no inheritance apart from their association with Joshua, who is a figure of Jesus, whose Hebrew name is Joshua. This explains why Israel said they had no inheritance in David during the split of the kingdom. Their inheritance was through association with Ephraim the firstborn, just as our inheritance is through association with Jesus the firstborn.
So when all Israel saw that the king hearkened not unto them, the people answered the king, saying, What portion have we in David? neither have we inheritance in the son of Jesse: to your tents, O Israel: now see to thine own house, David. So Israel departed unto their tents. 1 Kings 12:16
And why Ezekiel describes Israel as Ephraim (the firstborn) and his associates
Say unto them, Thus saith the Lord GOD; Behold, I will take the stick of Joseph, which is in the hand of Ephraim, and the tribes of Israel his fellows, and will put them with him, even with the stick of Judah, and make them one stick, and they shall be one in mine hand. Ezekiel 37:19
When Abraham set this up only God walked between the halves.
That's possible, but Abraham could have and probably did walk between them. I mean he was right there setting everything up, so it would have been a natural thing for him to walk between the pieces. But God was indeed the only one who bound himself to do anything