I am not sure if something similar to this has already been posted, but I decided to post my way of adding video textures to games. It is the quickest and simplest way I have found so far.
Note: Video textures do NOT play sound, but it can be added later by extracting the sound from the video and playing it with a sound actuator.
@MarcoIT: I actually wrote the script a while back when I was figuring out how to use the video texture module. The one from Tutorialforblender3d must do the same thing. I shall then use the tutorialsforblender3d script (as it will probably be better). I’ll re-upload a new one with their script. Thanks for telling me that there’s a similar script.