Chief of Security sounds good for such a high-ranking redshirt, as any Engineering role would have him outrank ol' Scotty. Odds are, the previously seen Security Chief Giotto of the same rank would either have been smart enough to apply for a transfer, or would be late, and not just from this meeting...
High-ranking goldshirts other than Kirk have been seen in TOS before, but IIRC only on three occasions.
-In "Where No Man Has Gone Before", Spock shared the command gold with Kirk in his apparent role of First Officer.
-In "Court Martial" the Records Officer of the ship, Lieutenant Commander Finney, wore gold. One might surmise that "Records Officer" is the traditional if somewhat outdated name for the hyper-important guy who is in charge of the ship's computer... A high rank indeed would be warranted, then.
-In "Arena", Kirk beams down to the Gorn trap with what he calls his "Tactical Officers". The party includes one blueshirt Lieutenant (Kelowitz), one redshirt Ensign (O'Herlihy), and one goldshirt Lieutenant Commander (Lang). Assuming that poor doomed O'Herlihy was just honorary escort, we could say that Lang was a hands-on kind of Tactical Officer, in charge of the big guns of the ship, or tactical planning, or whatnot. Kelowitz might have been more of a theoretician.
So our "Enterprise Incident" goldshirt might be a Second Officer, and perhaps Sulu's superior in the Helm department or Chekov's in Navigation. Since he has never pulled bridge duty, though, it's likelier that he'd be one of the two "specialist" goldshirt types: a Records Officer or a Tactical Officer. Perhaps he does take charge of the bridge at times, but only on those shifts where Kirk is asleep? Or perhaps he spends all his time supervising the computer department or fussing over the phaser banks?
Plotwise, I guess it would make the most sense if the person present in this briefing were the Tactical Officer.
Timo Saloniemi