In the interview transcript Majorie Wimpole refers to Eugene in the past tense; the source does not specify what has become of him, or the status of their relationship at any time. If Eugene lived with his family he resided in the Farside Base, on the far side of Luna.
The character of Eugene, the dates (given as a century earlier than the contemporary interpretation of Star Trek history), and many other facts in Star Trek II Biographies point to it being in a radically different continuity from most other sources. Later works (starting in 1986 in TOS novel: Enterprise: The First Adventure) established George Samuel Kirk, Sr. as the father of James T. Kirk, which was canonised in the 2009 movie Star Trek. Other alternative Kirk fathers include Benjamin Kirk, from the Gold Key Comics Psycho-File, and George Joseph Kirk, from Academy: Collision Course.