As implied by Iceag, Steam games use a media viewer based on the OS player. If the media player is not up to date, no video for you.
If it's not enough to fix it, i recommend you to verify the fragmentation of game files (through the property menu). It'll solve fragmentations problems, and check for damaged files, so it may fix your problem too.
If these actions don't fix your issue, and you don't mind not seeing the intro, you should put
-novideo in the launch options (through the property menu). It will result in not displaying the video, and directly load the game.
If you really want to see the intro, and none of the two first solutions worked, you can still try to uninstall/reinstall the game.