How to transform GUI Texture?

From the video, I have trouble identifying what you are drawing that is not being transformed. And from your title and your keywords, I'm not sure what you are talking about. Unity has a GUI system. It has a GUI.DrawTexture() which displays textures in screen coordinates. Moving the camera or changing the field of view will not impact images drawn with GUI.DrawTexture. You of course can manually resize them. Unity also as a GUITexture that is not part of the GUI system. GUITextures live in Viewport space where (0,0) is the lower left of the screen and (1,1) is in the upper right. They are also unaffected by camera movement and camera field of view changes. Likewise, you can manually resize them.

If you want a texture displayed that lives in world space and therefore is impacted by camera movement and zooming, you should use a Plane or the new Quad.