Do you have John's father as Thomas Games or Gaines?
This is what I have in my notes --
same book, pp. 23-25. p. 134 27 September 1673. I THOMAS GAINES of the County of Rappahannock doe give unto JOHN GAINES my Son, one Mare Colt and appoint my Brother in Law, WILLIAM JOHNSON, to be Feoffe in Trust
From [Old] Rappahannock County Deed Book, 1672-1676