You can't, which ultimately is the point. AE has no way of being "aware" of motion in video. You have to use tracking.
Mocha should do a decent job with the shot you've got there. But, depending on the camera movement, you might be able to use AE's built-in corner pin tracker. You could use CC Power Pin to get more control of the end result of either one.
If that was my project I never would have put green on the screen. It just adds work that is completely unnecessary and less you have something very complicated going on in front of the screen. Also, if you leave the screen black by keeping the set turned off you can pick up reflections in the room and add them with blend mode to any video you composite. Those kind of details make the composite much more believable. This is nothing more than simple corner pin tracking you can do it in After Effects or Mocha.