What did Rosicky do today?

I think Darkness already answered it.
Let's get a couple of things straight:
- The modern game is tactical, with speed and technique (not in the sense of dribbling ability) added in.
- More important than dominate a game is to control it, especially in competitions like these and in first games, where you want to save energies for the rest of the competition.
- A game is controlled by how well the collective movements and especially positioning are done. For example, the czechs have a leftwinger with 34 years old, that has lot the edge for a long time ago, but because of how well organised the team is, he does not need to run a lot or get more tired than normally expected. He was very much on game for 82 minutes.
The czechs didn't destroy the USA, they didn't even outplayed them in the sense of putting the oppoennt out of breath. What they did was a nice display of modern positional play. That way they won the game comfortably and with minimum energy expended. Not necessarily enough to win the WC, but enough for today. And Rosicky was very much involved in all of it, he and Nedved were the pivots of the system, but Rosicky shined more because when it's necessary to run and press the speed button, he's one that does it because he's the youngest of the lot.
So far, the czechs and the dutch were the best, or if you prefer, the most consistent.