If the video you're making is a "transformative work" (i.e. it's your own unique gameplay, you're putting your own commentary over it and/or you're showing clips to illustrate a point), it falls under fair use laws. Therefore, it would not fall under typical copyright law. That's how most people who make game-related videos structure their videos.
As it is, the only time any of this was ever enforceable was if a stingy copyright holder (Rockstar, notably) pulled videos to keep spoilers of their games for leaking out. Otherwise, most (if not all) companies look the other way and let you run rampant if you're doing walkthroughs, LP's or commentary. Other industries are a different matter (you can't upload an episode of, say, America's Next Top Model and earn money off it through AdSense), but transformative works for games are pretty clear.