you just need to download the mvdemo.war file, and deploy it the same way you deployed mapviewer.ear. Just make sure a) it is deployed to the same domain/server where mapviewer is running, and b) it uses '/mvdemo' as the context path (which should be the default).
Prior to the deployment you can unpack the contents of mvdemo.war into a directory named mvdemo.war/ and deployed from that open directory, or just deploy the un-exploded .war file directly. Both should work.
After the app is deployed and started, point your browser to http://localhost:<port>/mvdemo to access it.