Primogeniture was the law in South Carolina from 1712 until 1791. From a quick reading of your abstracts it would appear that Hugh Ross' (aka Hugh Ross, Jr) father (H.R., Sr) died intestate before 1791. Similar primogeniture "heir at law" statements were not uncommon in South Caroline deeds and included to establish ownership of the granter.
A form of primogeniture was practiced after 1791 to the extent that the eldest son was bequeathed all of the real property by the will, with allowances for the widow during her lifetime or widowhood. This was simply a throw back to the old tradition of first born son gets it all.