There is a discussion going on the Digra games network mailing list on what to call games within games. Intradiegetic games was deemed too cumbersome. Other perfectly sensible suggestions have been staged games, minigames and embedded games. However, Robby Ratan won that round with his brilliant coinage: ga-game-me.
When Harmonix gets around to publishing DragStarHero, my handle is totally going to be Lady Gagememe.