If the video clip is longer than 15 seconds, we dim the stage and house lights while it plays. This does require communication between the slide person and the light board operator (on headset), and it's a good idea for all to know what the "out" or ending section of the clip is to avoid a dark, dead-space after it plays.
We also learned (the hard way) that, even though no lights are pointed at the screen, our light-colored stage carpet reflects a tremendous amount of light up onto the screen. Front projected images are more susceptible to this "light pollution" than are rear projected. Keep your stage lighting as far away from the screen as possible. Dim as many lights as you can during the message (if you use slides) and dip to nearly blackout on the video clips.