It might in the future, according to one reading of Senate Bill 978, assuming it gets passed. This is a proposed law put before the Senate about a couple months ago, but the games community just sat up and noticed once it read the language and understood the totality of its prohibitions.
The proposed law is ostensibly meant to criminalise streaming copyrighted content (an act currently subjected to civil law provisions only). So S.B. 978 defines that behaviour as a performance of copyrighted material, and defines a performance as "10 or more public performances by electronic means, during any 180-day period, of 1 or more copyrighted works." Do the imbeciles who wrote this language even use YouTube? That's practically the entire service.
This is a lay opinion only, but if the bill becomes law and someone goes to federal pound-me-in-the-ass prison for putting Grand Theft Auto IV multiplayer on Ustream, I foresee an immediate challenge on grounds of fair use, not to mention a big argument over what a performance is—code on a video game, or the unique actions the user makes with it.
Advocates for S.B.978 stress that they're just trying to "harmonize" the criminal code with the civil code. Currently only copying and distributing copyrighted works can actually get you landed in jail. Why a criminal penalty is necessary now is a rhetorical question answered with "Because the recording industry and filmmaking lobbies have given lawmakers a bunch of money to see that it happens."
What's more likely is this is a tool for use in selective enforcement. A how-to guide for L.A. Noire won't get someone in trouble, but a leaked trailer will. Best of all, corporate counsel doesn't have to file the case. Just hand the matter over to the feds and they'll handle everything from investigation to the costs of trying the case. Given that we've seen takedowns of uncomplimentary videos on copyright grounds, who knows how far this will reach.
While I'd like to think that everyone's overreacting a bit and that there is no way game video uploads are meant to be prosecuted, knowing how colossally fucked-up and straight-up bribed the U.S. Congress is, the concern is understandable.