Video will only play on the animation timeline, not in frame animation.
Frame animation is designed to animate things frame by frame. So you'd have to advance the video manually to get it to play in frame animation. You can do this by copying and pasting individual images, but it is slow and choppy.
If you want to animate layers that aren't the video, and still have the video play, you'll need to stay in the timeline animation panel and use keyframes. You can click the arrow to the left of the layer, then create keyframes for the position, opacity and/or the styles. Do this by clicking the stopwatch moving the time to another point, then changing the layer. It looks like this: