Unity has updated basic support for video playback on textures in Unity WebGL.
Unity’s built-in MovieTexture class is not currently available for the WebGL platform. However, it is simple and efficient to use the browser’s built-in html5 video element to render video to a texture instead. This package provides a basic implementation of a MovieTexture class on WebGL using html5 video, with support for basic playback controls (play/pause/seek).
See the contained VideoTest.cs script for a simple sample of playing back video on a texture with a basic UI allowing playback control.