The first game that comes to mind is Elite Beat Agents on DS. 2006 was a stacked year, but I truly believe that relatively modest rhythm game should be in GOTY contention.
But to answer your question, I don't think it's possible for such a game to win the plurality of GOTY awards. Genres like RPG and action-adventure tend to dominate awards season. I think GOTY voters want adventure, and a story, and a meaty single-player campaign to dig their teeth into.