It really depends on the content of the video. It sounds like you're talking about doing a Let's Play or a livestream (such as Twitch) of a game. The law really hasn't caught up with technology in this regard, so there's not really any brightline rules that say that it's OK. However, the general consensus among the game industry is that LP's and livestreams are non-infringing activities, and that general industry practice is to allow these sorts of things (which are good PR anywayfor the game's IP rightsholders). YouTube policy also permits Let's Play-type videos, but under their policies you may need permission from the game's publisher to monetize videos that contain copyrighted material. Additionally, you'll need to be careful about licenses for any background music you have going on (such as music in your credits/intro/outro).
I focus my practice on (video) gaming industry, casino gambling, and complex internet law issues, electronic free speech, entertainment law, copyright and trademark law, and computer fraud. I primarily represent game developers and founders of emergent internet technologies. The author is a Maryland attorney; however no answer given on Avvo is intended as legal advice or intended to create an attorney-client relationship.
This is a trickier area of copyright law than it should be. Pursuant to Section 106 of the Copyright Act, publicly displaying or performing a copyrighted work is infringement of the copyright. However, Section 107 states that doing so for commentary or criticism is fair use and is not considered infringement. It seems straightforward, but then there are some factors that come into consideration that can make it complicated. For the most part, if your commentary or criticism is the predominant part of your videos then you are more likely in fair use. But, that doesn't mean your videos won't be taken down by YouTube's automatic copyright enforcement program or if a rights holder points you out. For video game content, most fair uses are fighting an uphill battle on the internet if the copyright holder wants to fight them.
Not a real clear issue that can be given a short answer. Based to be done is a limited amount.
Most lawyers will give you a free consultation if you ask for one. We do this all the time, but remember that our time is valuable and you should stay with the people who help you the most.