There is an article on Star Trek time travel in *the Best of Trek # 2 * in which it is concluded that it is impossible to know what happened to Captain Christopher and the guard. The article says that beaming human bodies into spaces already occupied by human bodies would be deadly, for reasons that should be obvious.
In Menagerie part 2":
NUMBER ONE: Now, you all know the situation. We're hoping to transport down inside the Talosian community.
SPOCK: If our measurements and readings are an illusion also, one could find oneself materialised inside solid rock.
In "Return to Tomorrow":
SCOTT: I don't like it, sir. The transporter co-ordinates preset by an alien of some sort. You could materialise inside solid rock.
MCCOY: Inside solid rock?
SPOCK: Unlikely. These co-ordinates correspond with the location of the subterranean chamber.
In "Tomorrow is Yesterday" our heroes say they are going to beam two persons into the the space occupied by their past bodies - which should be just as deadly as beaming into solid rock - and do seem to beam those two persons SOMEWHERE. And yet the bodies they are allegedly beamed into don't turn into horrors out of the infamous Star Trek: the Motion Picture transporter sequence.
Thus something else, somewhere on the spectrum from wonderful to horrifying, must have happened to Captain Christopher and the air force guard.
There is no evidence that Kirk, Spock, & co. planned to dispose of their guests and were lying about what they planned to do. But their plan made no sense. Thus they seem to have been under some influence that made them think a senseless plan would work, and under that influence they seemed to beam their guests SOMEWHERE.
For the sake of Captain Christopher and the Air Force Guard, we can only hope that mysterious unknown mental influence had a decent fate planned for them.
Thus the question of why Captain Christopher forgot everything he experienced aboard the Enterprise is based on the false presumption that the future Captain Christopher was beamed into the space occupied by the past Captain Christopher. That could not possibly have resulted in both or either of his selves surviving - and we did see one of them surviving the experience.