If you've ever been "roused" out of your sleep by someone, then you'll have no trouble seeing that rousing refers to anything that gets you going, up on your feet, energized.
There's nothing like a rousing tournament of Twister to get you off your butt and into the game. Cheerleaders and rock stars are in the business of creating rousing spectacles. They want their audiences to get up on their feet, clap their hands, and get on the bandwagon. A good drinking song, too, is rousing, inspiring folks to clink their glasses, sway back and forth, and, well, keep drinking. Beethoven was a master of music that was thoughtful one minute and rousing the very next.