So I did some experimenting and got a video to play. There may be other methods, but this one worked the first time I tried it.
Add the video file to your project files and also add the browser object to your project. Use the browser object to load the video.
Browser > Go to URL (or a new window/optional) > type the name of your video file in the quotes. Example: if you added the video, "vid.mp4" then type that exactly in the quotes. The video should play fine with sound and whatnot.
One way to use this to show videos is to have a hidden layer with a black background that hides the rest of the layout and display the video on top of this; alternately, you could just load it in a different layout.
Does anyone know a way, using the browser object and URL, to control the size of the video? If we could, we might use this method to display a video on an in-game TV, for example.
The other issue is the video files are usually very large, so optimizing the format and keeping the video length small is crucial.
EDIT: this was done with r119 and Chrome. I'm guessing the video will have to be in a format compatible with browsers. I have no idea if there is a "universal" format that all browsers recognize.