I think the events of the past few months speak for themselves, but in case they don't: gamers have demonstrated they are a virulent hate group and a general drain on society.
This measure would solve multiple problems affecting America today:
1. the problem of gamer "culture"
2. the lack of a halfways-decent space program
3. violent crime (video games have been proven to correlate with violence)
4. net neutrality (gamers not downloading terabytes worth of hentai anymore = less strain on internet providers)
5. at least one terrorist movement (#gamergate) would be destroyed, maybe others as well
6. the economy (no gamers = greatly increased productivity)
Some other problems would be solved as well, but I have a limited amount of space.
In closing: there are literally no downsides.