Even if they can't take Europe, the RIAA will not give up on the USA, which is under no such commitments. Plus, they will probably learn from the outcome in the EU and modify their public campaign in the US accordingly.
Sad to say, but these are the kinds of rights and freedoms which get more respect in Europe than here (which as I mention: the US is the stronghold of intellectual property rights legislation). If the US can force this down the throats of enough non-EU countries (eg Costa Rica -- these countries will go like dominoes because they have no choice. Also, many small developing world governments would love to impose laws whereby they can spy on your hard drive and will participate eagerly), they have some chance of eventually turning a table and presenting EU policy as the exception, thereby stirring up the right wing in Europe to correct the situation.
If you don't think the video game industry would set it's sights higher than just catching people who cheat on-line, you are hopelessly naive. They are digging in for a long term complex fight over file sharing.