Without convencional 'goals', nongames should find other ways of rewarding the player and giving him a sense of progression within the game. Unlocking features would be a reasonable answer, but based on what? Since most gaming devices are equiped with clocks and calendars, time and weather could be a solution.
I will start playing Animal Crossing, which utilizes these very resources to create a persistent world. I am struggling with similar issues regarding my MA project, and I expect to find ideas on that game.