Does rule of thirds apply to videos?
It is basically the same.
In a movie, you should have a motivated camera.
Meaning that the camera itself has or delivers an emotion.

A simple example:
Place someone really small into a corner of the screen, darken the lights. The person will look depressed and pushed to the edge from society.

Place someone in the entire frame into the middle and film them slightly from below and they will look powerfull and important.

You don't need to allways use rule of thirds in film, but you should consider it.

For example bringin an emotion into walking scene:

Person in right thirds, walking to left; Looks like the person walks into an open world
Person in right thirds, walking to right; Wlaking against a wall, not comming further...

There can be much meaning hidden inside a camera framing/move