There is a space after you finish a game in which to write your own annotations to each move. Is it a good idea to replay your game, remembering why you made a move and what its impact was, and trying to do the same for the computer's move and using this space to record those observations? Or what is the best way to learn from the games you play? I've been away from chess for some time and am playing terribly. Is there even any point for me to review my currently terrible games?

Of course there is, everyone does it, even in grandmaster matches you will see the players keeping notes after each move they make. I guess even for them it's hard to remember the entire game by heart.
The game chart usually tells you when you blunder, apart from that you can send the game to the training mode and let the mentor lines analyze the positions you think you need to study.
The mentor lines are the main reason people use a chess software like chessmaster and fritz.