Instead of "playing" the video games, try analyzing them. Look at them like a programmer, like you would any other program. Think about how every frame would be coded, for instance, say you're making asteroids. Think down to just one frame. You have the ship in the middle, the asteroids flying around, the score and lives at the top. There you go, you have a few objects already. Now unpause that, and you have animation. Well, all that is is just a continuous loop that has changes in every iteration, depending on what happens in the game. You also have the controller, so there's input to worry about. And, of course, the screen, so you have to draw to that. When you destroy an asteroid, they would split or be destroyed, and your score would go up. Destroy them all, and you get to the next level, or new frame/scene. When you die, your lives would be reduced by one, and when you run out of lives, the game loop ends. You can either restart it, or close it all together.
So basically, you just have to scrutinize every aspect of a game. Think about it like a programmer, not a gamer, and you should be all set. I'm sure there are plenty of books on the subject as well. Have fun!