Bones, Spock. since you are playing this tape, we will assume that I am dead, that the tactical situation is critical, and both of you are locked in mortal combat.
What did that mean? As a kid, I could think of only one meaning: Bones and Spock would be at each other's throats, even during a crisis, if there were no Kirk to mediate between them. Not literally, but they'd be arguing. Mortal combat was a hyperbole.
Now I'm not so sure, because it seems presumptuous for Kirk to think that. Maybe he meant "You two will be fighting to save the ship against whatever it was that killed me."
I never had a doubt as a kid, but now I don't know. How did you take it back then, and now as an adult?