Theater
Each button plays its own video, and the lights dim when playback starts. Examples for VRChat's video player and for ProTV.
With VRChat's video player
Play buttons
Add a Tripwire Trigger to each button.
Watching together
VRChat's video players don't sync playback by themselves: as above, the video plays only for whoever pressed. To play it for everyone, set the card to Everyone's screen in Advanced settings; players who join later still won't get it. For that, a player with its own sync, such as ProTV, is the reliable choice.
Dimming the lights
Add a Tripwire Trigger to the video player's own object (Screen): video events only reach triggers on that object.
With ProTV
Give each play button Use another script with the object holding TVManager as its target, and pick Play URL in Use.
The lights can listen from a trigger on any object.
Lights in step for everyone
ProTV and similar players sync playback for everyone. Each screen dims its lights when it gets the notification, so the lights agree without a synced variable.