So there are some things you will need to understand about Source Engine models.
1) The only native animations you can export are Skeletal Animations (by bones). Your scene is animated at the vertex level via the Cloth modifier. There is no way to get your actual animation into Source. It's just not supported.
2) There is a way to get Vertex Animation into Source but it is not the same as your animation in the scene. The vertex animation that you can get into Source is called a Flex. These are controlled via Morpher or Morph-O-Matic modifiers inside Max. Even though you can get these kinds of morphs into Max, they are not the same as your keyframe animated vertex animations. Instead, they are morph controls to use with things like facial animations. See
Making Facial Animations.
Here is another discussion similar to yours on our forums:
https://www.wallworm.net/index.php?topic=1127.0