Yuk, the diagram Mangetout is badly mislabelled. The screen on the floor is not reflective. It is dispersive, it is a simple projection screen. If it were reflective the audience would simply see the projector in the on-stage screen, and the beam of light emanating from the projector’s lens. But with a simple projection screen on the floor, and the mylar screen angled at about 45 degrees, the image on the projection screen is seen vertical and as if it were on the stage.
Choosing a stretched mylar screen is useful for a number of reasons. An important one is that it is very thin. Reflections come from both surfaces of the screen, but since the screen is so thin they are indistinguishable. A glass sheet will have two surfaces, and if you are close enough you will see two images offset very slightly. On stage this will not matter too much, but is a consideration. Mylar also stretches very flat. So much so that you can make an almost perfect mirror stretching aluminised mylar on a frame. Such mirrors are used to reflect light from projectors where you need to fold the optical path to get space use down. Rear projection systems and virtual reality system use them. Getting a glass pane this perfect would be quite difficult. Especially in large sizes. (I have a couple of such mirrors that were originally constructed for VR systems. They are uncanny. What you see in them is utterly real, in comparison an ordinary rear surface silvered glass mirror is so obviously flawed you wonder how you put up with them.)