I know nothing about the current state of military tech, but that looks like a targeting camera that has some sort of edge detection allowing it to track the object.

The vertical lines to the left and right of the object appear computer controlled, to me, especially because they track the left and right edges of the object and the vertical length changes in a way that seems reactive to the object on screen.

The brief moment where those lines don't have the object centered and then it just jumps back into place (at the very end of the video ~31-32s) screams computer assisted to me.

In short, I don't think that's manual tracking, because I'm pretty sure that even a Navy pilot would have trouble tracking it that perfectly by hand.